Question

A parallelogram has sides with lengths of `14` and `9`. If the parallelogram's area is `49`, what is the length of its longest diagonal?

Answer 1

Length of its longest diagonal is `20.98`

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 `9` and area is `49` we have

`14xx9xxsintheta=49` or `sintheta=49/(14xx9)=7/18`

`costheta=sqrt(1-(7/18)^2)=sqrt(1-49/324)`

= `sqrt(275/324)=1/18sqrt275=16.583/18=0.9213`

Then larger diagonal of parallelogram would be given by

`sqrt(a^2+b^2-2abcostheta)=sqrt(14^2+9^2+2xx14xx9xx0.9213`

= `sqrt(196+81+252xx0.9213)=sqrt(208+232.1676)`

= `sqrt440.1676=20.98`