Question

1. 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. a. solve the formula for ℓ. 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: $\ell=\frac{P - 2w}{2}$.

Step3: Substitute values for part b

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

Step4: Simplify the expression for part b

First, calculate $2\times4 = 8$. Then $36-8 = 28$. Finally, $\frac{28}{2}=14$.

Answer:

a. $\ell=\frac{P - 2w}{2}$
b. 14 meters