Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `90`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `26.09`

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 `15` and `12` and area is `90` we have

`15xx12xxsintheta=90` or `sintheta=90/(15xx12)=1/2`

`costheta=sqrt(1-(1/2)^2)=sqrt(1-1/4)=sqrt(3/4)=sqrt3/2`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(15^2+12^2+2xx15xx12xxsqrt3/2`

= `sqrt(225+144+180xx1.732)=sqrt(369+311.76)`

= `sqrt680.76=26.09`