Question

the length of a rectangle is 4 less than four times the width. if the perimeter of the rectangle is 128, find the width of the rectangle.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 4w - 4$.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 4w - 4$ and $P = 128$ into the formula: $128=2((4w - 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $128 = 2(5w - 4)$. Then distribute the 2: $128=10w - 8$.

Step4: Solve for $w$

Add 8 to both sides of the equation: $128 + 8=10w$, so $136 = 10w$. Divide both sides by 10: $w=\frac{136}{10}=13.6$.

Answer:

$13.6$