Question

A parallelogram has sides with lengths of `12` and `6`. If the parallelogram's area is `48`, what is the length of its longest diagonal?

Answer 1

Longest diagonal of the parallelogram is `16.95`

Explanation:

Area of a parallelogram whose sides are `a` and `b` and included angle `theta` is `axxbxxsintheta`

Hence, in the given instance `12xx6xxsintheta=48`

or `sintheta=48/(12xx6)=2/3`

Longest diagonal `L` of the parallelogram will be given by cosine formula

`L=sqrt(a^2+b^2+2abcostheta)`

As `costheta=sqrt(1-(2/3^2)=sqrt(1-4/9)=sqrt5/9=1/3sqrt5`

Hence, `L=sqrt(12^2+6^2+2xx12xx6xx1/3sqrt5)`

= `sqrt(144+36+48sqrt5=sqrt(180+48xx2.236)=sqrt287.328=16.95`