Question

solve each of the real - world scenarios using literal equations:
a rectangular living room has a perimeter of 108 feet. if the width is 22 feet, what is the length?
(perimeter of a rectangle = 2w + 2l)
32 feet
42 feet
64 feet
86 feet

Explanation:

Step1: Substitute the known values into the formula

Given \(P = 108\) (perimeter) and \(W=22\) (width), and the formula \(P = 2W+2L\). Substitute: \(108=2\times22 + 2L\).

Step2: Simplify the equation

First, calculate \(2\times22 = 44\). The equation becomes \(108=44 + 2L\).

Step3: Isolate the term with \(L\)

Subtract \(44\) from both sides: \(108 - 44=44 + 2L-44\). So, \(64 = 2L\).

Step4: Solve for \(L\)

Divide both sides by \(2\): \(\frac{64}{2}=\frac{2L}{2}\). Thus, \(L = 32\).

Answer:

32 feet