Question

the length of a rectangle is nine inches more than four times the width. the perimeter is 58 inches. find the length and width. the length is blank inches, and the width is blank inches.

Explanation:

Step1: Define variables

Let the width be \( w \) inches. Then the length \( l = 4w + 9 \) inches.

Step2: Use perimeter formula

The perimeter of a rectangle is \( P = 2(l + w) \). Given \( P = 58 \), substitute \( l \):
\( 58 = 2((4w + 9) + w) \)

Step3: Simplify the equation

Simplify inside the parentheses: \( 58 = 2(5w + 9) \)
Divide both sides by 2: \( 29 = 5w + 9 \)
Subtract 9: \( 20 = 5w \)
Divide by 5: \( w = 4 \)

Step4: Find length

Substitute \( w = 4 \) into \( l = 4w + 9 \): \( l = 4(4) + 9 = 16 + 9 = 25 \)

Answer:

The length is 25 inches, and the width is 4 inches.