Question

part a rectangles the formula p = 2l + 2w represents the perimeter of a rectangle. in this formula, l is the length of the rectangle and w is the width. solve the formula for l. part b find the length when the width is 4 meters and the perimeter is 36 meters.

Explanation:

Step1: Isolate terms with $\ell$

Given $P = 2\ell+2w$, subtract $2w$ from both sides: $P - 2w=2\ell$.

Step2: Solve for $\ell$

Divide both sides by 2: $\ell=\frac{P - 2w}{2}$.

Answer:

for Part A:
$\ell=\frac{P - 2w}{2}$

Step1: Substitute values

We know $P = 36$ and $w = 4$. Substitute into $\ell=\frac{P - 2w}{2}$, so $\ell=\frac{36-2\times4}{2}$.

Step2: Calculate

First, calculate the numerator: $36-2\times4=36 - 8 = 28$. Then, $\ell=\frac{28}{2}=14$.