Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `180`, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal `d_1 = 19.2094`

Explanation:

Area of parallelogram is `l * h`

`h = (Area) / l = 180 / 15 = 12`

`sin theta = h /w = 12/12 = 1` Since w = h.
`theta = pi/2`

It’s a rectangle and both the diagonals are equal.

Length of diagonal `d = sqrt(l^2+w^2) = sqrt(15^2 + 12^2) = 19.2094`