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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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.
Tiffany
4.5103 Answers
1. Let the width of the rectangle be w
2. Then the length of the rectangle is 3w + 9
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
Length: l = 42
2. Then the length of the rectangle is
3. The formula for the perimeter of a rectangle is
4. Substituting the given perimeter and expressions for length and width:
5. Simplifying the equation:
6. Subtract 18 from both sides:
7. Divide both sides by 8:
8. Now calculate the length using
9. Therefore, the dimensions are:
Width:
Length:
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