SOLUTION: The perimeter of a rectangle is 68cm. If the diagonal is 26cm, find the dimensions of the rectangle.

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Question 530769: The perimeter of a rectangle is 68cm. If the diagonal is 26cm, find the dimensions of the rectangle.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
perimeter = 2(a +b), where a = length and b = width
p = 68
a+b = 34
so
a = 34-b
.
diagonal = c = 26 cm
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Pythagorean Theorem teaches us that:
.
c^2 = a^2 + b^2
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Substitute for a = 34-b and c = 26
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26^2 = (34-b)^2 + b^2
,
Collect terms.
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676 = (b^2 -68b + 1156) + b^2
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2b^2 -68b + 480 = 0
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b^2 -34b +240 = 0
.
+graph%28500%2C500%2C-20%2C40%2C-60%2C40%2Cx%5E2-34%2Ax%2B240%29+
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Factor
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(b-10)(b-24) = 0
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b = 10 or 24
a = 34 -b
so
a = 24 or 10 respectively
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Either way, the two sides of the rectangle are 10 and 24.
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Checking, we find:
10^2 + 24^2 = 26^2
100 + 576 = 676
True
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Answer: The rectangle has dimensions of 10 by 24 cm.
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Done.