Question

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

Answer 1

Length of its longest diagonal is `32.96`

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 `24` we have

`24xx9xxsintheta=24` or `sintheta=24/(24xx9)=1/9`

`costheta=sqrt(1-(1/9)^2)=sqrt(1-1/81)`

= `sqrt(80/81)=1/9sqrt80=8.9443/9=0.9938`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(24^2+9^2+2xx24xx9xx0.9938`

= `sqrt(576+81+432xx0.9938)=sqrt(657+429.3216)`

= `sqrt1086.3216=32.96`