SOLUTION: The longer side of a rectangle is four times the length of the shorter sides. If the diagonal is 17 cm long, find the dimensions of the rectangle.

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Question 1152871: The longer side of a rectangle is four times the length of the shorter sides. If the diagonal is 17 cm long, find the dimensions of the rectangle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
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W = width
L = length = 4W
D = diagonal = 17

Using the pythagorean theorem, we find that,
a^2 + b^2 = c^2
L^2 + W^2 = D^2
(4W)^2 + W^2 = 17^2
16W^2 + W^2 = 289
17W^2 = 289
17W^2 = 289
W^2 = 289/17 ... divide both sides by 17
W^2 = 17
W = sqrt(17) ... apply square root to both sides
4W = 4sqrt(17) ... multiply both sides by 4
L = 4sqrt(17)

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Answer:

The exact dimensions of the rectangle are: 4sqrt(17) cm by sqrt(17) cm cm

The approximate dimensions of the rectangle are: 16.492 cm by 4.123 cm

since,
sqrt(17) = 4.123
4sqrt(17) = 16.492
approximately