Question

use a formula from geometry to solve for the unknown quantity. the length of a rectangle is 9 feet longer than the width. if the perimeter is 110 feet, find the length and width of the rectangle. the width of the rectangle is 23 feet. (type an integer or a decimal.) the length of the rectangle is (type an integer or a decimal.) feet square feet cubic feet

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ feet. Then the length $l$ is $w + 9$ feet.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 110$ feet, we substitute $l=w + 9$ into the formula: $110=2((w + 9)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $110=2(2w + 9)$. Then distribute the 2: $110 = 4w+18$.

Step4: Solve for $w$

Subtract 18 from both sides: $110-18=4w$, so $92 = 4w$. Divide both sides by 4: $w=\frac{92}{4}=23$ feet.

Step5: Solve for $l$

Since $l=w + 9$, substitute $w = 23$ into the equation: $l=23 + 9=32$ feet.

Answer:

The width of the rectangle is 23 feet and the length of the rectangle is 32 feet.