Question

A parallelogram has sides with lengths of `9` and `8`. If the parallelogram's area is `18`, what is the length of its longest diagonal?

Answer 1

Find the height. Use Pythagoras twice: to find how far the base extends, and then to find the length of the longer diagonal.
`d = 16.86`

Explanation:

Draw a sketch of the parallelogram first!

Find the height of the parallelogram. A = b x h

`h = A/b = 18/9 =2`

The endpoint of the top line of the parallelogram is vertically above the base extended.
We need to calculate the length of the extended line, let's call it `x`.

Working in the right-angled triangle outside the parallelogram with
Hypotenuse = 8 and height = 2 , gives the following:

`x^2 = 8^2 - 2^2 = 60`
`x = sqrt60 " "` leave it in this form

Length of the extended base = `9 + sqrt60~~16.746....`

Now work with the right-angled triangle with the longer diagonal`(d)` as the hypotenuse, and the two shorter sides being `2 and (9+sqrt60)`

`d^2 = (9+sqrt60)^2 +2^2 =284.427....`

`d = 16.86`