Find Side BC in Parallelogram: Perimeter = 30 cm with Side CD = 2x

Question

How long is side BC given that the perimeter of the parallelogram is 30 cm?

$CD=2x$

00:00 Find BC

00:04 The perimeter of the parallelogram equals the sum of the sides

00:07 The perimeter of the parallelogram equals the sum of the sides

00:11 We'll substitute appropriate values according to the given data, and solve for BC

00:20 We'll isolate BC

00:35 And this is the solution to the question

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:

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

$BC = 15 - 2x$

Therefore, the correct option is:

This matches the problem's given correct answer.

$15-2x$