Question

A parallelogram has sides with lengths of `14` and `15`. If the parallelogram's area is `63`, what is the length of its longest diagonal?

Answer 1

Find the height, then use Pythagoras in two different right-angled triangles to get the length of the longer diagonal
`d =28.66`

Explanation:

Draw a sketch of the parallelogram first, extend the base and draw in the height to meet the extended base. There are two right-angled triangles formed.

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

`h = A/b = 63/15 = 21/5 = 4.2`

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 = 14 and height = 4.2, gives the following:

`x^2 = 14^2 -4.2^2 = 178.36`
`x = sqrt178.36 " "` leave it in this form

Length of the extended base = `15 + sqrt178.36~~28.355`

Now work with the right-angled triangle with the longer diagonal`(d)` as the hypotenuse, and the two shorter sides being `4.2 and (15+sqrt178.36)`

`d^2 = (15+sqrt178.36)^2 +4.2^2 =821.654....`

`d = 28.66`