Question

A parallelogram has sides with lengths of `14` and `12`. If the parallelogram's area is `84`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `25.12`

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 `12` and area is `84` we have

`14xx12xxsintheta=84` or `sintheta=84/(14xx12)=1/2`

`costheta=sqrt(1-(1/2)^2)=sqrt(1-1/4)=sqrt(3/4)=sqrt3/2=1.732/2=0.866`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(14^2+12^2+2xx14xx12xx0.866`

= `sqrt(196+144+336xx0.866)=sqrt(340+290.976)`

= `sqrt630.976=25.12`

Length of its longest diagonal is `25.12`