# A parallelogram has sides with lengths of 24  and 9 . If the parallelogram's area is 96 , what is the length of its longest diagonal?

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Dec 10, 2017

Length of the longest diagonal AC is 32.3109

#### Explanation:

Given $l = 24 , w = 9 , A r e a = 96$

Area of the parallelogram = l * h = 96
$\therefore B E = C F = h = \frac{A r e a}{l} = \frac{96}{24} = 4$

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 4^2) = 8.0623

AF = l + a = 24 + 8.0623 = 32.0623

Longest diagonal AC = sqrt(AF^2 + CF^2) = sqrt(32.0623^2 + 4^2) = 32.3109

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