Question

A parallelogram has sides with lengths of `16` and `5`. If the parallelogram's area is `48`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `20.22`

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 `5` and area is `48` we have

`16xx5xxsintheta=48` or `sintheta=48/(16xx5)=3/5`

`costheta=sqrt(1-(3/5)^2)=sqrt(1-9/25)`

= `sqrt(16/25)=4/5`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcosthet)=sqrt(16^2+5^2+2xx16xx5xx4/5`

= `sqrt(256+25+128)=sqrt409`

= `20.22`