The sides of the rectangular trapezoid are 15 cm and 17 cm, the middle line is 6 cm. Find the base of the trapezoid.

Let’s denote the trapezoid by ABCD. Let’s omit the height СN.

Consider a triangle NСD.

СN = AB = 15 cm.

1. Let’s define ND.

ND2 = CD2 – CN2;

ND2 = 172 – 152 = 289 – 225 = 64;

ND = √64 = 8 cm.

2. Let’s define the side of BC.

(BC + AD): 2 = 6 (middle line);

AD = AN + ND;

AN = BC;

AD = BC + ND;

(BC + BC + 8): 2 = 6;

BC = 6 – 4;

BC = 2 cm.

3. Let’s define the AD side.

AD = 8 + 2 = 10 cm.

Answer: the sides of the base of the trapezoid are BC = 2 cm, AD = 10 cm.