# The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25.

The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25. Find the second side of the trapezoid.

Let us lower the height CH from the top of the trapezoid.

The area of the trapezoid is: S = (AD + BC) * CH / 2.

300 = (34 + 6) * CH / 2.

CH = 600/40 = 15 cm.

In the triangle СНD, we define, according to the Pythagorean theorem, the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

DН = 20 cm.

Determine the length of the segment AK.

AK = AD – KH – DH = 34 – 6 – 20 = 8 cm.

In a right-angled triangle ABK, we determine the length of the hypotenuse AB.

AB ^ 2 = BK ^ 2 + AK ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289.

AB = 17 cm.

Answer: Lateral side AB = 17 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.