The lateral sides of a rectangular trapezoid are 15 cm and the middle line is 6 cm to find the base of the trapezoid.

Let us draw the height of CH from the top of C to the base of the AD. In a right-angled triangle CHD, the hypotenuse CD = 17 cm, and the leg CH = AB = 15 cm.Then, according to the Pythagorean theorem, DH ^ 2 = CD ^ 2 – CH ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64 …
DN = 8 cm.
Let the smaller base BC = X cm, then the larger base AD = X + DH = X + 8 cm.
The average length of a trapezoid is equal to half the sum of the lengths of its bases. MK = (BC + AD) / 2 = (X + X + 8) / 2 = 6 cm.
2 * X = 2 * 6 – 8 = 4.
X = 4/2 = 2 cm.
BC = 2 cm.
AD = 2 + 8 = 10 cm.
Answer: The bases of the trapezoid are 2 cm, 10 cm.