Question

A parallelogram has sides with lengths of `21` and `12`. If the parallelogram's area is `84`, what is the length of its longest diagonal?

Answer 1

`32.6`

Explanation:

ABCD is the parallelogram.

Parallelogram area `A_P=b×h`
where b=base, h=height

Given `A_P=84 and b=12⇒h=84/12=7`

Note that triangle CDE is a right-angled triangle :
`⇒x=sqrt(21^2-7^2)=sqrt392=19.8`

Now we can see that the longer diagonal `AC` is also the hypotenuse of the right-angled triangle ACE:

`=> AC =sqrt((12+19.8)^2+7^2)=32.6`