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 (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 $l = w + 9$ feet.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 110$ feet, we substitute $l$ and $P$ 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 $l=w + 9$, then $l=23 + 9=32$ feet.

Answer:

The width of the rectangle is 23 feet.