Question

1. the perimeter of a rectangle is given by the formula, $p = 2l + 2w$, where $l$ is the length and $w$ is the width. which of the following shows the correct formula solved for $l$?

a. $l = p + 2w$
b. $l = p - 2w$
c. $l = \frac{p + 2w}{2}$
d. $l = \frac{p - 2w}{2}$

Explanation:

Step1: Start with the perimeter formula

We have the formula \( P = 2l + 2w \). Our goal is to solve for \( l \). First, we need to isolate the term with \( l \) on one side. So, we subtract \( 2w \) from both sides of the equation.
\( P - 2w = 2l + 2w - 2w \)
Simplifying the right side, the \( 2w \) and \( -2w \) cancel out, leaving us with \( P - 2w = 2l \).

Step2: Solve for \( l \)

Now, to get \( l \) by itself, we divide both sides of the equation \( P - 2w = 2l \) by 2.
\( \frac{P - 2w}{2} = \frac{2l}{2} \)
Simplifying both sides, the 2 in the numerator and denominator on the right side cancels out, giving us \( l=\frac{P - 2w}{2} \).

Answer:

D. \( l=\frac{P - 2w}{2} \)