Question

A parallelogram has sides with lengths of `24` and `9`. If the parallelogram's area is `14`, what is the length of its longest diagonal?

Answer 1

`color(red) (32.986)` (approx.)

Explanation:

Since the `"Area"` is given as `14` (sq.units)
and (relative to side with length `24`) `"Area" = 24 xx h`

`rarr h= 14/24= 7/12`

By the Pythagorean Theorem
`color(white)("XXX")x=sqrt(9^2-(7/12)^2) ~~8.981076` (with calculator)

and the longest diagonal is
`color(white)("XXX")d=sqrt((24+x)^2+h^2)`

`color(white)("XXXX")=sqrt(32.981076^2 + (7/12)^2)`

`color(white)("XXXX")~~32.98623` (again, with calculator)