Question

1. a rectangle has perimeter 24 feet. if the length is (x + 3) feet and the width is x feet, write and solve an equation to find x.

Explanation:

Step1: Write the perimeter formula for a rectangle

The perimeter formula for a rectangle is \(P = 2(l + w)\), where \(P\) is the perimeter, \(l\) is the length, and \(w\) is the width. Given \(P = 24\), \(l=x + 3\), and \(w=x\), we substitute these values into the formula: \(24=2((x + 3)+x)\).

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \((x + 3)+x=2x + 3\). So the equation becomes \(24 = 2(2x+3)\). Then, divide both sides of the equation by 2: \(\frac{24}{2}=\frac{2(2x + 3)}{2}\), which simplifies to \(12=2x+3\).

Step3: Solve for \(x\)

Subtract 3 from both sides of the equation: \(12-3=2x+3 - 3\), so \(9 = 2x\). Then divide both sides by 2: \(x=\frac{9}{2}=4.5\).

Answer:

\(x = 4.5\)