Given a rectangle ABCD, side BC-20cm, diagonal AC-25cm. Find the side of the CD.

A diagonal divides a rectangle into two identical right-angled triangles. We know one leg and the hypotenuse of the right-angled triangle ABC. Let’s find the leg AB according to the Pythagorean theorem (the sum of the squares of the legs in a right-angled triangle is equal to the square of the hypotenuse):

a² + b² = c²;

AB² + BC² = AC²;

AB² + 20² = 25²;

AB² + 400 = 625;

AB² + 400 = 625;

AB² = 625 – 400;

AB² = 225;

AB = √225;

AB = 15 cm.

In a rectangle, opposite sides are equal and parallel. Therefore:

CD = AB = 15 cm.

Answer: 15 cm