Perimeter of a Parallelogram: Calculate The Missing Side based on the formula

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information and formula.

• Step 2: Apply the perimeter formula for a parallelogram.

• Step 3: Solve for the unknown side length.

Let's work through each step:

Step 1: We are given that the perimeter of the parallelogram is 30 cm and one side $AB = 9$ cm. We need to find the other side, $b$.

Step 2: The perimeter formula for a parallelogram is $P = 2(a + b)$, where $a = 9$ cm and the perimeter $P = 30$ cm.

Step 3: Substitute the known values into the formula:

$30 = 2(9 + b)$

Divide both sides by 2 to simplify:

$15 = 9 + b$

Subtract 9 from both sides to solve for $b$:

$b = 15 - 9$
$b = 6$

Therefore, the length of the other side is $\text{6 cm}$.

Thus, the solution to the problem is $b = 6$ cm.

Let's solve this problem step-by-step:

• Step 1: Understand the problem
  We are given the perimeter of the parallelogram as 25 cm and one side $AB$ as 8 cm. We need to calculate the length of the other side of the parallelogram, $BC$.

• Step 2: Recall the formula for the perimeter of a parallelogram
  The perimeter $P$ of a parallelogram is given by:
  $P = 2(a + b)$
  Where $a$ and $b$ are lengths of adjacent sides.

• Step 3: Apply the given information
  We have $P = 25$ cm and one side $a = AB = 8$ cm. Substitute these into the formula:
  $25 = 2(8 + b)$

• Step 4: Solve for the unknown side $b$
  First, divide both sides by 2:
  $12.5 = 8 + b$
  Subtract 8 from both sides:
  $b = 12.5 - 8$
  $b = 4.5$

• Therefore, the length of the other side is $4.5$ cm.

Upon checking with the given choices, the correct answer is indeed 4.5.

To solve this problem, follow these steps:

• Step 1: Identify the given information: one side $AB = 4 \, \text{cm}$, and the perimeter $P = 12 \, \text{cm}$.

• Step 2: Apply the perimeter formula for parallelograms, $P = 2a + 2b$.

• Step 3: Solve for the other side $b$.

Now, let's work through the calculations:

The formula for the perimeter of a parallelogram is:
$P = 2a + 2b$
Given $a = 4 \, \text{cm}$ and $P = 12 \, \text{cm}$, substituting these values gives:
$12 = 2(4) + 2b$
Simplifying, we have:
$12 = 8 + 2b$
Subtract 8 from both sides:
$4 = 2b$
Divide both sides by 2 to find $b$:
$b = 2$

Therefore, the length of the other side is $2 \, \text{cm}$.

To solve this problem, we'll use the perimeter formula for a parallelogram, which is:

$P = 2(a + b)$

where $P$ is the perimeter, $a$ is the length of one side, and $b$ is the length of the adjacent side.

Given:

• Perimeter, $P = 60 \, \text{cm}$
• One side, $AB = 20 \, \text{cm}$

Let's apply these values to the formula:

$60 = 2(20 + b)$

To isolate $b$, we first divide both sides by 2:

$30 = 20 + b$

Now, solve for $b$ by subtracting 20 from both sides:

$b = 10 \, \text{cm}$

Therefore, the length of the other side is 10 cm.

To solve this problem, we will calculate side $CD$ using the perimeter formula of a parallelogram:

• The perimeter formula of a parallelogram is $P = 2 \times (AB + CD)$.
• Given $P = 45$ cm and $AB = 15$ cm, substitute these values into the equation: $45 = 2 \times (15 + CD)$.
• Simplify the expression: $45 = 30 + 2 \times CD$.
• Rearrange the equation to solve for $CD$: $2 \times CD = 45 - 30$.
• This simplifies to: $2 \times CD = 15$.
• Divide both sides by $2$ to find $CD$: $CD = \frac{15}{2}$.
• Thus, $CD = 7.5$ cm.

Therefore, the length of side $CD$ is $7.5$ cm.

To solve this problem, we need to calculate the length of side $CD$ given the perimeter and one side length.

Step 1: Identify the given information. We know that the perimeter $P$ of the parallelogram is 22 cm, and one of the sides, $AB$, is 8 cm.

Step 2: Apply the perimeter formula for a parallelogram, which states that $P = 2(AB + BC)$. Since $AB = CD$ and $BC = DA$ (opposite sides are equal), we have:

$22 = 2(8 + CD)$.

Step 3: Solve for $CD$. First, simplify the equation:

$22 = 2(8 + CD)$.

$22 = 16 + 2 \cdot CD$.

$22 - 16 = 2 \cdot CD$.

$6 = 2 \cdot CD$.

Divide both sides by 2 to find $CD$:

$CD = \frac{6}{2} = 3$ cm.

Therefore, the length of side $CD$ is $3$ cm, which corresponds to choice 1.

To solve this problem, we'll use the formula for the perimeter of a parallelogram:

• Step 1: Identify the given information:
  The perimeter $P$ is 70 cm, and the side $AB = 20$ cm.
• Step 2: Apply the perimeter formula:
  The formula for the perimeter of a parallelogram is $P = 2(a + b)$, where $a$ and $b$ are the lengths of adjacent sides.
• Step 3: Set up the equation:
  Let $CD = x$. Then, the equation becomes: $70 = 2(20 + x)$
• Step 4: Solve for $x$:
  Divide both sides by 2: $35 = 20 + x$ Subtract 20 from both sides: $x = 15$

Therefore, the length of side CD is $15$ cm.

To solve for the side $CD$ in the given parallelogram:

• Step 1: Identify the given information: the perimeter $P = 15 \, \text{cm}$ and side $AB = 5 \, \text{cm}$.
• Step 2: Apply the perimeter formula for a parallelogram $P = 2(a + b)$.
• Step 3: Relate the perimeter to the given sides. Set $a = AB = 5 \, \text{cm}$ and $b = CD$.

Substituting into the formula, the equation is:

$15 = 2(5 + CD)$.

Simplify and solve for $CD$:

$15 = 10 + 2CD$.

Subtract 10 from both sides:

$5 = 2CD$.

Divide both sides by 2:

$CD = \frac{5}{2} = 2.5 \, \text{cm}$.

Therefore, the length of side $CD$ is $2.5 \, \text{cm}$.

By calculating, the correct answer choice is: $2.5 \, \text{cm}$.

To solve the problem, we'll proceed as follows:

• Step 1: Identify the known values and write down the perimeter formula: The perimeter of a parallelogram is $2(a + b)$, where $a = 7$ cm is the known side, and $b$ is the unknown side.
• Step 2: Substitute the known perimeter into the formula: We know that $2(a + b) = 20$.
• Step 3: Set up the equation with known values: $2(7 + b) = 20$.
• Step 4: Solve the equation for $b$: Start by simplifying $2(7 + b) = 20$ to $14 + 2b = 20$.
• Step 5: Subtract 14 from both sides to isolate $2b$: $2b = 20 - 14$. Thus, $2b = 6$.
• Step 6: Divide both sides by 2 to solve for $b$: $b = \frac{6}{2} = 3$ cm.

Therefore, the length of the other side is $3$ cm.

To solve this problem, we'll identify the values and apply the perimeter formula specific to parallelograms.

• Step 1: Identify the given values.
• Step 2: Apply the perimeter formula for a parallelogram.
• Step 3: Solve for the unknown side.

Now, let's work through each step:

Step 1: We know $AB = 15$ cm and the perimeter of the parallelogram is 40 cm. Assume $CD = x$ cm (since in a parallelogram opposite sides are equal, $CD = DA$ and $AB = BC$).

Step 2: The formula for the perimeter of a parallelogram is $2(a + b)$, where $a$ and $b$ are the lengths of any two adjacent sides.

Step 3: Plugging in the known values, we have $2(15 + x) = 40$.

Simplify and solve for $x$:

$30 + 2x = 40$

$2x = 40 - 30$

$2x = 10$

$x = \frac{10}{2} = 5$

Therefore, the solution to the problem is $\text{side } CD = 5 \text{ cm}$.

Checking the multiple-choice answers, option 4 matches our solution:

$5$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the appropriate formula
• Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us that the parallelogram has a total perimeter of 35 cm and one side $AB = 9.5$ cm.
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$, where $a$ and $b$ are adjacent sides. Here, given that $AB = 9.5$ cm, we have $a = 9.5$ cm.
Step 3: Substitute the known values into the formula:
$35 = 2(9.5 + b)$
Divide both sides by 2:
$17.5 = 9.5 + b$
Solve for $b$:
$b = 17.5 - 9.5 = 8$

Therefore, the length of side $BC$ is $\mathbf{8}$ cm.

To solve this problem, let's follow these steps:

• Step 1: Calculate the length of $CD$ using the given $X = 2$.
• Step 2: Use the perimeter formula for the parallelogram to find $AB$.
• Step 3: Solve for the unknown length $AB$.

Step 1: Calculate the length of $CD$.

Given $X = 2$, we find $CD = 3X = 3 \times 2 = 6$ cm.

Step 2: Use the formula for the perimeter of a parallelogram:
$P = 2 \times (AB + CD)$.

Substitute the given values:
$40 = 2 \times (AB + 6)$.

Step 3: Solve for $AB$.

Start by dividing the entire equation by 2:
$20 = AB + 6$.

Subtract 6 from both sides to isolate $AB$:
$AB = 20 - 6 = 14$.

Therefore, the length of side $AB$ is $14$ cm.

Each pair of opposite sides are parallel and equal.

AB is parallel to DC and therefore also AB = DC = 8.

We will use the given perimeter to find AD and BC—which are also equal and parallel to each other.

Let's now calculate the perimeter of the parallelogram:

$24=2AB+2AD$

$24=16+2AD$

$24-16=2AD$

$8=2AD$

Then, we'll divide the two sides by 2:

$\frac{8}{2}=\frac{2AD}{2}$

$AD=4$

To solve this problem, we'll follow these steps:

• Step 1: Use the perimeter formula for the parallelogram.
• Step 2: Substitute the known values and solve for $x$.

Now, let's work through each step:

Step 1: The formula for the perimeter of a parallelogram is given by:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of the sides. In this case, we have:

$a = 15$ and $P = 36$.

Step 2: Substitute the values into the perimeter formula:

$36 = 2(15 + x)$

We can simplify this equation to solve for $x$:

$36 = 30 + 2x$

Step 3: Subtract $30$ from both sides:

$36 - 30 = 2x$

$6 = 2x$

Step 4: Divide both sides by $2$ to solve for $x$:

$x = \frac{6}{2}$

$x = 3$

Therefore, the solution to the problem is $x = 3$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the known value of one side and the perimeter.
• Step 2: Use the perimeter formula to set up an equation.
• Step 3: Solve for the unknown side $x$.

Now, let's work through each step:
Step 1: The problem gives us a perimeter $P = 54$ and one side of the parallelogram as 7.
Step 2: Using the formula for the perimeter of a parallelogram $P = 2(a + b)$, we have:

$2(x + 7) = 54$

Step 3: Simplify and solve for $x$:

Divide both sides by 2:

$x + 7 = 27$

Subtract 7 from both sides to isolate $x$:

$x = 27 - 7$

Simplifying, we obtain:

$x = 20$

Therefore, the solution to the problem is $x = 20$.

To solve this problem, we'll follow these steps to find $x$:

• Step 1: Use the formula for the perimeter of a parallelogram.
• Step 2: Set up an equation involving $x$ and solve for $x$.
• Step 3: Substitute the values and perform calculations to find $x$.

Let's proceed:

Step 1: The formula for the perimeter of a parallelogram is:
$P = 2(a + b)$ where $a$ and $b$ are the lengths of two adjacent sides. Here, $a = x$ and $b = x+1$.

Step 2: According to the problem, the perimeter $P = 42$. Therefore, we set up the equation:
$42 = 2(x + (x + 1))$

Step 3: Simplify and solve for $x$:
$42 = 2(2x + 1)$
$42 = 4x + 2$
Subtract 2 from both sides:
$40 = 4x$
Solve for $x$ by dividing both sides by 4:
$x = 10$

Therefore, the solution to the problem is $x = 10$.

To calculate $x$ in the given parallelogram, we begin by noting the given perimeter formula for the parallelogram, $P = 2(a + b)$.

The two sides, as given, are $a = x$ and $b = 3x$. Substituting these into the formula gives:

$P = 2(x + 3x)$

We know the perimeter $P = 20$, therefore:

$2(x + 3x) = 20$

Simplifying inside the parentheses, $x + 3x = 4x$, we rewrite the equation as:

$2 \times 4x = 20$

Which gives:

$8x = 20$

To solve for $x$, divide both sides by 8:

$x = \frac{20}{8}$

Simplifying gives:

$x = \frac{5}{2}$

Or, $x = 2.5$.

Thus, the value of $x$ is $\boxed{2\frac{1}{2}}$.

To solve this problem, we begin by using the formula for the perimeter of a parallelogram:

The perimeter $P$ is given by: $P = 2(a + b)$

Given: $P = 30 \text{ cm}$, and $CD = 2x$. We know $AB = 2x$ since opposite sides of a parallelogram are equal. So, we write:

• $P = 2(BC + CD) = 30$
• $2(BC + 2x) = 30$
• $BC + 2x = 15$ (after dividing both sides by 2)
• $BC = 15 - 2x$

Thus, the length of side $BC$ is given by:

$BC = 15 - 2x$

Therefore, the correct option is:

• Choice 1: $15 - 2x$

This matches the problem's given correct answer.