Question

A parallelogram has sides with lengths of `16` and `9`. If the parallelogram's area is `54`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `24.576`

Explanation:

Area of a parallelogram is given by `axxbxxsintheta`,

where `a` and `b` are two sides of a parallelogram and `theta` is the angle included between them.

As sides are `16` and `9` and area is `54` we have

`16xx9xxsintheta=54` or `sintheta=54/(16xx9)=3/8`

`costheta=sqrt(1-(3/8)^2)=1/8sqrt55=0.927`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcos150^@)=sqrt(16^2+9^2+2xx16xx9xx0.927`

= `sqrt(256+81+288xx0.927)=sqrt(337+266.976)`

= `sqrt603.976=24.576`