Triangle Perimeter Practice Problems - Step-by-Step Solutions

To find the perimeter of triangle $\triangle ABC$, we need to sum the lengths of its sides:

• Side $AB = 3$
• Side $BC = 4$
• Side $CA = 5$

Using the formula for the perimeter of a triangle:

$\text{Perimeter} = AB + BC + CA$

Substitute the known values:

$\text{Perimeter} = 3 + 4 + 5$

$\text{Perimeter} = 12$

Thus, the perimeter of triangle $\triangle ABC$ is $\mathbf{12}$.

From the multiple-choice options provided, the correct choice is option 1: 12.

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

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

Now, let's work through each step:
Step 1: The problem gives us the lengths of two adjacent sides of the parallelogram: $a = 10$ and $b = 8$.
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$.
Step 3: Plugging in our values, we get:

$P = 2(10 + 8) = 2 \times 18 = 36$

Therefore, the perimeter of the parallelogram is $36$.

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

• Step 1: Identify the given information.
• Step 2: Apply the perimeter formula for a triangle.
• Step 3: Perform the addition to find the perimeter.

Now, let's work through each step:

Step 1: We have the lengths of the sides of $\triangle ABC$ as follows:
$AB = 7$, $BC = 14$, and $CA = 8$.

Step 2: We'll use the formula for the perimeter of a triangle, which is the sum of its side lengths:
$P = AB + BC + CA$.

Step 3: Plugging in the values, we calculate:
$P = 7 + 14 + 8 = 29$.

Therefore, the perimeter of $\triangle ABC$ is $\textbf{29}$.

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:

• Step 1: Identify the side lengths of the trapezoid:
  Top side $= 10$, Bottom side $= 5$, Left side $= 10$, Right side $= 11$.
• Step 2: Apply the perimeter formula:
  The formula for the perimeter $P$ of a trapezoid is $P = a + b + c + d$.
• Step 3: Perform the calculations:
  Substitute the given lengths into the formula:
  $P = 10 + 5 + 10 + 11 = 36$.

Therefore, the perimeter of the trapezoid is $36$.

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of all its sides. The steps are as follows:

• List the lengths of the sides: the bases are $10$ and $12$, and the two non-parallel sides are each $7$.
• Apply the perimeter formula for a trapezoid: $P = a + b + c + d$.
• Substitute the given values into the formula: $P = 10 + 12 + 7 + 7$.
• Calculate the sum: $P = 10 + 12 + 7 + 7 = 36$.

Therefore, the perimeter of the trapezoid is $36$.

This matches the correct answer choice from the provided options.