In a right-angled triangle ABCD, the diagonals intersect at the point O. AO = 10 cm, AD = 16 cm. Calculate the AB side.

In a rectangle, the diagonals are equal and at the point of intersection they are divided in half, then the triangle AOD is isosceles. Let us draw the AOD in the triangle and draw the height OH, which is also the median of the triangle. Then, according to the Pythagorean theorem OH^2 = OA^2 – AH^2 = 100 – 64 = 36.

OH = 6 cm.Then moan AB = 2 * OH = 2 * 6 = 12 cm.

Answer: Side AB is 12 cm.