Question

I’m confused on this one

Answer 1

It's a parallelogram so if one angle is 90 degrees they all will be because of transverse angles and all that good stuff.

So we're given the diagonal of a rectangle and one side and we're asked to find the other. The diagonal of a rectangle is the hypotenuse of the right triangle whose legs are the sides of the rectangle. So this is a Pythagorean Theorem question in disguise:

$AB^2 + AD^2 = BD^2$

$AD^2 = BD^2 - AB^2$

$AD = \sqrt{ BD^2 - AB^2 }$

$AD = \sqrt{149^2 - 51^2} = \sqrt{19400} = 140$

Answer: 140 cm

I don't recall seeing this Pythagorean Triple before.