Question

6.3 factor special products homework
score: 19/25 answered: 19/25
question 20
the length of a rectangle is six inches more than ten times the width. the perimeter is 232 inches. find the length and width.
the length is inches, and the width is inches.
question help: written example
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Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) inches. Then the length \( l=(10w + 6) \) inches.
The formula for the perimeter of a rectangle is \( P = 2(l + w) \). Given \( P=232 \) inches.

Step2: Substitute into the perimeter formula

Substitute \( l = 10w+6 \) and \( P = 232 \) into \( P=2(l + w) \):

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Step3: Solve for \( w \)

Subtract 12 from both sides: \( 232-12=22w \), so \( 220 = 22w \).
Divide both sides by 22: \( w=\frac{220}{22}=10 \) inches.

Step4: Solve for \( l \)

Substitute \( w = 10 \) into \( l=10w + 6 \): \( l=10\times10+6=106 \) inches.

Answer:

The length is \( 106 \) inches, and the width is \( 10 \) inches.