Question

A parallelogram has sides with lengths of `16` and `6`. If the parallelogram's area is `48`, what is the length of its longest diagonal?

Answer 1

`2 sqrt 73`

Explanation:

/_/ ABCD

`|AB| = 16, |BC| = 6 \Rightarrow |CD| = 16, |DA| = 6`

`sin`  `angle DAB = |DH| / |DA| = h / 6`, DH perpendicular to AB

Area = `1/2 * |AB| * h = 1/2 * 16 * 6 * sin angle DAB = 48`

`sin angle DAB = 48/(8*6) \Rightarrow  = 90º`

Rectangle. Pythagora.

`|AC| = |BD| = x, 16^2 + 6^2 = x^2 = 256 + 36 = 292`

`x = sqrt 292`