# algebra and trigonometry

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find the dimensions of a rectangle having perimeter 14m and diagonal of length 5m

• algebra and trigonometry -

Let the diagonal be c and the sides a and b
b = sqrt (c^2 - a^2) = sqrt(25-a^2)

Perimeter = 2a + 2b = 2a + 2sqrt (25-a^2) = 14
14 - 2a = 2 sqrt (25-a^2)
196 - 56a + 4a^2 = 4(25-a^2) = 100 -4a^2
8a^2 -56a +96 = 0
a^2 -7a + 12 = 0
(a-3)(a-4) = 0
The side lengths are 3 and 4

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