Question

A parallelogram has sides with lengths of `9` and `8`. If the parallelogram's area is `16`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `16.9`

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 `9` and `8` and area is `16` we have

`9xx8xxsintheta=16` or `sintheta=16/(9xx8)=2/9`

`costheta=sqrt(1-(2/9)^2)=sqrt(1-4/81)`

= `sqrt(77/81)=1/9sqrt77=8.775/9=0.975`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2+2abcostheta)=sqrt(9^2+8^2+2xx9xx8xx0.975`

= `sqrt(81+64+144xx0.975)=sqrt(145+140.4)`

= `sqrt285.4=16.9`