In a rectangular trapezoid, the base = 5cm and 17cm, and the side side is 13 cm, find the height.

Let us denote the trapezoid by the letters ABCD, where AD – base equal to 17, BC – base equal to 5, CD – side equal to 13.
We need to find the height or side of AB
1) We draw a perpendicular (CH) from point C to the side AD, we denote this value as x, it will be equal to the height and side AB
2) Find HD
HD = 17-5 = 12
2) We get a right-angled triangle HCD
By the Pythagorean theorem, we find the desired leg
x ^ 2 = 13 ^ 2-12 ^ 2
x = Under the root (13-12) * (13 + 12) = root of 25 = 5
Answer: 5