Question

A parallelogram has sides with lengths of `9` and `8`. If the parallelogram's area is `48`, what is the length of its longest diagonal?

Answer 1

`15.885`

Explanation:

`ABCD` is the parallelogram.

Parallelogram Area `A_P=bxxh`
In this case, `b=AD=8, h=CE`
`=> 48=8xxh => h=48/8=6`

Pythagorean theorem : `a^2=b^2+c^2`
`=> (CD)^2=(DE)^2+(CE)^2`
`=> DE=sqrt((CD)^2-(CE)^2)`
`=> DE=sqrt(9^2-6^2)=6.708`

Longer diagonal of the parallelogram = `AC`
`(AC)^2=(AE)^2+(CE)^2`
`AE=AD+DE=8+6.708=14.708`
`=> AC=sqrt(14.708^2+6^2)=15.885`