SOLUTION: If the diagonal of a rectangle has length 14 feet, and the area of the rectangle is 64 square feet, find the number of feet in the perimeter of the rectangle.
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Question 709063: If the diagonal of a rectangle has length 14 feet, and the area of the rectangle is 64 square feet, find the number of feet in the perimeter of the rectangle.
You can put this solution on YOUR website! If the diagonal of a rectangle has length 14 feet, and the area of the rectangle is 64 square feet, find the number of feet in the perimeter of the rectangle.
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Draw a rectangle with one diagonal.
Let the sides be L and W
Then diagonal = sqrt[L^2+W^2]
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Equations:
sqrt(L^2+W^2) = 14 ft.
L^2 + W^2 = 196
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LW = 64 sq. ft
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L = 64/W
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Substitute for "L" and solve for "W":
(64/W)^2 + W^2 = 196
64 + W^4 = 196W^2
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W^4 - 196W^2 + 64 = 0
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W^2 = 195.67
W = 13.99 ft
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Solve for L:
L = 64/W
L = 64/13.99
L = 4.57 ft
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Cheers,
Stan H.
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