Question

A parallelogram has sides with lengths of `5` and `9`. If the parallelogram's area is `36`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC `= color (purple)(12.6491)`

Explanation:

Given `l = 9, w = 5, Area = 36`

Area of the parallelogram = l * h = 36
`:. BE = CF = h = (Area)/l = 36 / 9 = 4`

AE = DF = a = sqrt(w^2-h^2) = sqrt(5^2 - 4^2) = 3#

AF = l + a = 9 + 3 = 12#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(12^2 + 4^2) = 12.6491#