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

Question 530769: The perimeter of a rectangle is 68cm. If the diagonal is 26cm, find the dimensions of the rectangle.
Answer by oberobic(2304) (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
.
Pythagorean Theorem teaches us that:
.
c^2 = a^2 + b^2
.
Substitute for a = 34-b and c = 26
.
26^2 = (34-b)^2 + b^2
,
Collect terms.
.
676 = (b^2 -68b + 1156) + b^2
.
2b^2 -68b + 480 = 0
.
b^2 -34b +240 = 0
.

.
Factor
.
(b-10)(b-24) = 0
.
b = 10 or 24
a = 34 -b
so
a = 24 or 10 respectively
.
Either way, the two sides of the rectangle are 10 and 24.
.
Checking, we find:
10^2 + 24^2 = 26^2
100 + 576 = 676
True
.
Answer: The rectangle has dimensions of 10 by 24 cm.
.
Done.
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