Question

the formula for the perimeter of a rectangle is ( p = 2l + 2w ), where ( l ) is the length of the rectangle and ( w ) is the width. you are given the perimeter and the width of a rectangle and you wish to solve for length. which of the following formulas is the correct solution for the length of the rectangle?

choose the correct answer below

( \bigcirc a ) ( l=\frac{p - w}{2} )
( \bigcirc b ) ( l=\frac{p}{2}+w )
( \bigcirc c ) ( l=\frac{p}{2}-w )
( \bigcirc d ) ( l = w-\frac{p}{2} )

Explanation:

Step1: Start with the perimeter formula

$$P = 2L+2W$$

Step2: Isolate the term with \(L\)

Subtract \(2W\) from both sides:
$$P - 2W=2L$$

Step3: Solve for \(L\)

Divide both sides by \(2\):
$$L=\frac{P - 2W}{2}=\frac{P}{2}-W$$

Answer:

C. \(L = \frac{P}{2}-W\)