Question

A parallelogram has sides with lengths of `9` and `8`. If the parallelogram's area is `36`, what is the length of its longest diagonal?

Answer 1

Longest diagonal = 15.4548

Explanation:

Area of parallelogram = l * h, where l is base and h is the corresponding height.

Given l = 9
`l * h = 36`

`h = 36 / 9 = 4`

`sin M = h / PM = 4/8 = 1/2 or /_ M = pi/6`

OM the largest diagonal = `h / sin (M/2)`

`OM = 4 / sin (pi/12) = 15.4548`