Question

A parallelogram has sides with lengths of `15` and `8`. If the parallelogram's area is `60`, what is the length of its longest diagonal?

Answer 1

22.29 approx

Explanation:

Let 'h' be the height of the parallelogram . Its area would thus be 15h=60 `->` h=4.

As shown in the figure below, `DE= sqrt (8^2- h^2) = sqrt (64-16)= sqrt48`

To find the longest diagonal AC, apply pythagoras theorem to right triangle ACE. Accordingly, `AC^2= h^2 +(15+sqrt48)^2`

`AC^2 = 16+225 +48 +30sqrt48 = 289+120sqrt3=`

AC= 22.29approx