Question

A parallelogram has sides with lengths of `12` and `8`. If the parallelogram's area is `60`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `18.92`

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 `12` and `8` and area is `60` we have

`12xx8xxsintheta=60` or `sintheta=60/(12xx8)=5/8`

`costheta=sqrt(1-(5/8)^2)=sqrt(1-25/64)`

= `sqrt(39/64)=1/8sqrt39=6.245/8=0.7806`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(12^2+8^2+2xx12xx8xx0.7806`

= `sqrt(144+64+192xx0.7806)=sqrt(208+149.8752)`

= `sqrt357.8752=18.92`