The sides of the rectangular trapezoid are 24cm and 25cm, the middle line is 12cm. Find the bases of the trapezoid.

Let’s draw the height of the trapezoid CH, CH = AB = 24 cm, since ABCH is a rectangle.

Then in a right-angled triangle СDН, according to the Pythagorean theorem, we determine the length of the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 25 ^ 2 – 24 ^ 2 = 625 – 576 = 49.

DН = 7 cm.

Let the length of the base BC = X cm, then the length of the base AD = (X + 7) cm.

Substitute the values into the formula for the midline of the trapezoid.

KP = (BC + AD) / 2.

12 = (X + X + 7) / 2.

2 * X = 24 – 7 = 17.

X = BC = 17/2 = 8.5 cm.

AD = 8.5 + 7 = 15.5 cm.

Answer: The lengths of the bases are 8.5 cm and 15.5 cm.