Question

1. the perimeter of the rectangle shown to the right is 96 feet. determine the length and width of the rectangle.

Explanation:

Step1: Write the perimeter formula

The perimeter formula of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Here, \(l=4x - 7\), \(w = x\), and \(P = 96\). So, \(96=2((4x - 7)+x)\).

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \((4x - 7)+x=5x - 7\). Then the equation becomes \(96 = 2(5x - 7)\). Divide both sides by 2: \(\frac{96}{2}=5x - 7\), which simplifies to \(48=5x - 7\).

Step3: Solve for \(x\)

Add 7 to both sides of the equation: \(48 + 7=5x\), so \(55 = 5x\). Then divide both sides by 5: \(x=\frac{55}{5}=11\).

Step4: Find the length and width

The width \(w=x = 11\) feet. The length \(l=4x - 7\). Substitute \(x = 11\) into the length formula: \(l=4\times11-7=44 - 7=37\) feet.

Answer:

The width of the rectangle is \(11\) feet and the length is \(37\) feet.