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

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.