Question

A parallelogram has sides with lengths of `5` and `9`. If the parallelogram's area is `27`, what is the length of its longest diagonal?

Answer 1

Longest possible diagonal measures 13.3417

Explanation:

Given `l = 9, w = 5, Area = 27`

Area of the parallelogram = l * h = 27
`:. BE = CF = h = (Area)/l = 27 / 9= 3`

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

AF = l + a = 9 + 4 = 13#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(13 ^2 + 3^2) = 13.3417#