Question

1. the length of a rectangle is 2 cm more than twice the width. the perimeter is 118 cm. what is the length of the rectangle?

parts:
total
equation:
solve:

Explanation:

Step1: Set up the equation for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width. Given that \(l=2w + 2\) and \(P = 118\). Substitute \(l\) into the perimeter formula: \(118=2((2w + 2)+w)\).

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \((2w + 2)+w=3w + 2\). So the equation becomes \(118 = 2(3w + 2)\). Then distribute the 2: \(118=6w+4\).

Step3: Solve for \(w\)

Subtract 4 from both sides: \(118 - 4=6w\), so \(114 = 6w\). Divide both sides by 6: \(w=\frac{114}{6}=19\).

Step4: Find the length \(l\)

Since \(l = 2w+2\), substitute \(w = 19\) into the formula: \(l=2\times19 + 2=38 + 2=40\).

Answer:

The length of the rectangle is \(40\) cm.