SOLUTION: The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.
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Question 201094: The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! The area fo a rectangle is 66ft squared and the diagonal of the rectangle is square root of 157 ft. What are the dimensions of the rectangle.
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Let x = width
and y = length
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Since we have two unknowns, we'll need two equations:
Equation 1:
xy = 66
Equation 2:
x^2 + y^2 = 157
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Solving equation 1 for y:
y = 66/x
Substituting the above into equation 2 we can solve for x:
x^2 + y^2 = 157
x^2 + (66/x)^2 = 157
x^2 + 4356/x^2 = 157
x^4 + 4356 = 157x^2
x^4 - 157x^2 + 4356 = 0
Factoring we get:
(x^2-121)(x^2-36) = 0
x = {11,6}
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Dimensions of rectangle are 11 feet by 6 feet
