Question

A parallelogram has sides with lengths of `15` and `12`. If the parallelogram's area is `54`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `26.69`

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 `15` and `12` and area is `54` we have

`15xx12xxsintheta=54` or `sintheta=54/(15xx12)=0.3`

`costheta=sqrt(1-(0.3)^2)=sqrt(1-0.09)`

= `sqrt(0.91)=0.954`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2+2abcosthet)=sqrt(15^2+12^2+2xx15xx12xx0.954`

= `sqrt(225+144+360xx0.954)=sqrt(369+343.44)`

= `sqrt712.44=26.69`