Question

question 1 of 13. step 1 of 1
the length of a rectangle is 9 feet more than the width. if the perimeter is 110 feet, what are the length and the width?
answer
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length: feet
width: 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 $P=2(l + w)$. Substitute $l = w + 9$ and $P = 110$ 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:

length: 32 feet
width: 23 feet