Question

A parallelogram has sides with lengths of `16` and `9`. If the parallelogram's area is `120`, what is the length of its longest diagonal?

Answer 1

Longest diagonal measures 22.2755

Explanation:

Given `l = 16, w = 9, Area = 120`

Area of the parallelogram = l * h = 120
`:. BE = CF = h = (Area)/l = 120 / 16 = 7.5`

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 7.5^2) = 4.9749#

AF = l + a = 16 + 4.9749 = 20.9749#

Longest diagonal AC `= sqrt(AF^2 + CF^2) = sqrt(20.9749^2 + 7.5^2) = 22.2755`