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The length of a rectangle is nine more than triple the width. If the perimeter is 106 inches, find the dimensions.

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Answer to a math question The length of a rectangle is nine more than triple the width. If the perimeter is 106 inches, find the dimensions.

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Tiffany
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103 Answers
1. Let the width of the rectangle be w inches.
2. Then the length of the rectangle is 3w + 9 inches.
3. The formula for the perimeter of a rectangle is P = 2l + 2w .
4. Substituting the given perimeter and expressions for length and width:
106 = 2(3w + 9) + 2w .
5. Simplifying the equation:
106 = 6w + 18 + 2w
106 = 8w + 18
6. Subtract 18 from both sides:
106 - 18 = 8w
88 = 8w
7. Divide both sides by 8:
w = 11
8. Now calculate the length using l = 3w + 9 :
l = 3(11) + 9
l = 33 + 9
l = 42
9. Therefore, the dimensions are:
Width: w = 11 inches
Length: l = 42 inches.

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