Question

A parallelogram has sides with lengths of `16` and `8`. If the parallelogram's area is `32`, what is the length of its longest diagonal?

Answer 1

`23.830`

Explanation:

As shown in the diagram, `ABCD` is the parallelogram.
Area of a parallelogram `A= bxxH`, where `b` is the base and `H` is the height.
Given that `AB=CD=8, AD=BC=16`, and area `A=32`,
`=> 32=8xxH, => H=4`

`DeltaBCE` is a right triangle.
Using Pythagorean theorem, we know that
`BC^2=CE^2+H^2`
`=> CE=sqrt(16^2-4^2)=sqrt240=4sqrt15`

`DeltaBDE` is also a right triangle.
`DB^2=DE^2+H^2`
`DE=DC+CE=8+4sqrt15=23.492`
`DB=sqrt(23.492^2+4^2)=23.830`

Hence, longest diagonal = `DB=23.830`