Question

A parallelogram has sides with lengths of `16` and `9`. If the parallelogram's area is `45`, what is the length of its longest diagonal?

Answer 1

`24.71`

Explanation:

As shown in the diagram, `ABCD` is the parallelogram.
Area of parallelogram `A=bxxH`
Given `b=9 and A=45`,
`=> H=45/9=5`
`DeltaBCE =` right triangle
`=> BC^2=BE^2+CE^2`, `(BC=16, BE=H=5)`
`=> CE=sqrt(16^2-5^2)=15.2`
`=> DE=DC+CE=9+15.2=24.2`

`DeltaBDE` is also a right triangle
`BD` is the hypotenuse and also the longer diagonal of the parallelogram.
`=> BD^2=BE^2+DE^2`
`=> BD=sqrt(5^2+24.2^2)=24.71`

Hence, the length of the longer diagonal =`BD=24.71`