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:
[tex]AB^2 + AD^2 = BD^2[/tex]
[tex]AD^2 = BD^2 - AB^2[/tex]
[tex]AD = \sqrt{ BD^2 - AB^2 }[/tex]
[tex] AD = \sqrt{149^2 - 51^2} = \sqrt{19400} = 140 [/tex]
Answer: 140 cm
I don't recall seeing this Pythagorean Triple before.
