Question

A parallelogram has sides with lengths of `24` and `9`. If the parallelogram's area is `144`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `31.29`

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 `24` and `9` and area is `144` we have

`24xx9xxsintheta=144` or `sintheta=144/(24xx9)=2/3`

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

= `sqrt(5/9)=1/3sqrt5=2.23607/3=0.7454`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(24^2+9^2+2xx24xx9xx0.7454`

= `sqrt(576+81+432xx0.7454)=sqrt(657+322.0128)`

= `sqrt979.0128=31.29`