Question

the formula for the perimeter of a rectangle is p = 2l + 2w where l is the length and w is the width. which equations are equivalent to the formula for the perimeter of a rectangle?
□ p = 2(l + w)
□ 2p = l + w
□ p - 2l = 2w
□ p - w = l
□ (p - 2w)/2 = l

Explanation:

Step1: Start with the formula $P = 2l+2w$.

This is the perimeter formula for a rectangle.

Step2: Factor out 2 on the right - hand side.

$P = 2(l + w)$ (by the distributive property $a\times b+a\times c=a(b + c)$, here $a = 2$, $b=l$, $c = w$).

Step3: Rearrange the formula $P = 2l+2w$ to solve for $l$.

First, subtract $2w$ from both sides: $P-2w=2l$. Then divide both sides by 2: $l=\frac{P - 2w}{2}$.

Answer:

$P = 2(l + w)$, $\frac{P - 2w}{2}=l$