Question

A parallelogram has sides with lengths of `14` and `8`. If the parallelogram's area is `49`, what is the length of its longest diagonal?

Answer 1

Find the height, then use Pythagoras twice - first to find the length of the extended base, then to find the length of the longer diagonal.
Diagonal = `sqrt461.425 = 21.48`

Explanation:

Draw a sketch of the parallelogram first!

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

`h = A/b = 49/14 = 7/2 = 3.5`

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 = 3.5 , gives the following:

`x^2 = 8^2 -3.5^2 = 51.75`
`x = sqrt51.75 " "` leave it in this form

Length of the extended base = `14 + sqrt51.75~~21.194`

Now work with the right-angled triangle with the longer diagonal`(d)` as the hypotenuse, and the two shorter sides being `3.5 and (14+sqrt51.75)`

`d^2 = (14+sqrt51.75)^2 +3.5^2 = 461.425....`

`d = 21.48`