Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `75`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `28.518`

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 `14` and `15` and area is `75` we have

`14xx15xxsintheta=75` or `sintheta=75/(14xx15)=5/14`

`costheta=sqrt(1-(5/14)^2)=1/14sqrt171=0.934`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcos150^@)=sqrt(14^2+15^2+2xx14xx15xx0.934`

= `sqrt(196+225+420xx0.934)=sqrt(421+392.28)`

= `sqrt813.28=28.518`