Question

question 1 - 5
the length of a rectangle is 50 centimeters longer than the width. if the perimeter of the rectangle is 220 centimeters, find the width and length
the width of the rectangle is centimeters
the length of the rectangle is centimeters

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) centimeters. Then the length \( l=w + 50 \) centimeters.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P = 2(l + w) \). Given \( P=220 \) centimeters. Substitute \( l = w + 50 \) into the formula: \( 220=2((w + 50)+w) \).

Step3: Simplify the equation

First, simplify the right - hand side: \( 220=2(2w + 50) \), then \( 220 = 4w+100 \).

Step4: Solve for \( w \)

Subtract 100 from both sides: \( 4w=220 - 100=120 \). Divide both sides by 4: \( w=\frac{120}{4}=30 \) centimeters.

Step5: Find the length

Since \( l=w + 50 \), substitute \( w = 30 \): \( l=30 + 50=80 \) centimeters.

Answer:

The width of the rectangle is 30 centimeters and the length is 80 centimeters.