Question

1. the length and width of a rectangle are consecutive even integers. the perimeter of the rectangle is 60 feet. find the length and width of the rectangle.

Explanation:

Step1: Define variables

Let the width be \( x \) (an even integer), then the length is \( x + 2 \) (consecutive even integer).

Step2: Use perimeter formula

The perimeter of a rectangle is \( P = 2(\text{length} + \text{width}) \). Substituting values: \( 60 = 2(x + (x + 2)) \).

Step3: Simplify equation

Simplify the right - hand side: \( 60 = 2(2x + 2)=4x + 4 \).

Step4: Solve for x

Subtract 4 from both sides: \( 60-4 = 4x\), so \( 56 = 4x \). Divide both sides by 4: \( x=\frac{56}{4}=14 \).

Step5: Find length

Length is \( x + 2=14 + 2 = 16 \).

Answer:

The width of the rectangle is 14 feet and the length is 16 feet.