Calculate Parallelogram Side Length: Given Perimeter 20cm and Side 7cm

A parallelogram has a perimeter of 20 cm

AB = 7 cm

Calculate the length of the other side.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:16 They are also a pair of opposite sides, therefore equal

00:21 The perimeter of the parallelogram equals the sum of its sides

00:37 Let's substitute appropriate values and solve for BD

00:57 Group the numbers into one factor, and BD into another factor

01:05 Isolate BD

01:20 This is the length of BD

01:26 And this is the solution to the question

Step-by-Step Solution

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.