Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `42`, what is the length of its longest diagonal?

Answer 1

Longest diagonal `d_1 = 26.82` units

Explanation:

`a = 15, b = 12, A_p = 42`

Applying Law of cosines,

Longest diagonal `d_1 = sqrt(a^2 + b^2 + (2 a b cos theta)` as `theta` is obtuse.

Area of parallelogram `A_p = a b sin theta`

`theta = sin ^-1 (A_p / ( a * b))`

`theta = sin ^-1 (42 / (15 * 12) ) = 0.2355^c`

`d_1 = sqrt(a^2 + b^2 + (2 a b cos theta))`

`d_1 = sqrt(15^2 + 12^2 + (2 * 15 * 12 * cos (0.2355))`

Longest diagonal `d_1 = 26.82` units