A little assistance please?

Question

It's some sort of derivation with the pythagorean theorem but I understand null. Any tips would be appreciated.

http://i295.photobucket.com/albums/mm142/SirScotty25/GeometryProblem.jpg

Answer 1

Solve for ?.  Let x = ?.

The large triangle ROK is a right triangle.  The two legs are:

OR = x + 5

OK = 13 + 5 = 18

The hypotenuse is:

KR = x + 13

By the Pythagorean Theorem we have:

(OR)² + (OK)² = (KR)²

(x + 5)² + 18² = (x + 13)²

x² + 10x + 25 + 324 = x² + 26x + 169

10x + 349 = 26x + 169

-16x = -180

x = -180/-16 = 45/4 = 11.25