Question

A parallelogram has sides with lengths of `5` and `9`. If the parallelogram's area is `32`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 13.0107

Explanation:

Given `l = 9, w = 5 Area = 32`

Area of the parallelogram = l * h = 32
`:. BE = CF = h = (Area)/l = 32 / 9 = 3.5556`

AE = DF = a = sqrt(w^2-h^2) = sqrt(5^2 - 3.5556^2) = 3.5154#

AF = l + a = 9 + 3.5154 = 12.5154#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(12.5154^2 + 3.5556^2) = 13.0107#