Question 204200: The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The area of a rectangle is 6, and its diagonal is sqrt{37}. Find its dimensions and perimeter
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Let x = width
and y = length
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From Pythagorean theorem
x^2 + y^2 = 37 (equation 1)
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From the area:
xy = 6 (equation 2)
Solve equation 2 for y:
y = 6/x
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Substitute aboe into equation 1 and solve for x:
x^2 + y^2 = 37
x^2 + (6/x)^2 = 37
x^2 + (36/x^2) = 37
x^4 + 36 = 37x^2
x^4 - 37x^2 + 36 = 0
(x^2-36)(x^2-1) = 0
x = {1, 6}
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Therefore, dimensions are
1 feet by 6 feet
Perimeter:
2(6+1) = 14 feet
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