Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `36`, what is the length of its longest diagonal?

Answer 1

There is a specific formula for this that can be derived from trigonometric theorems

Explanation:

`d_"long" = sqrt(b^2 + a^2 + 2b sqrt(a^2-(A/b)^2))`

where `a` and `b` are the sides and `A` is the area.

In this case:

`d_"long" = sqrt(225 + 144 + 2*12 sqrt(225-(36/12)^2)) = sqrt(369 + 24 sqrt(225 - 9)) = 26.86496832`