Find the diagonal AC of an isosceles trapezoid ABCD if you know that its bases are 7 and 25, and the side is 15.

Let’s draw two heights of the trapezoid from the obtuse angles ВK and CM. The KВСM quadrangle is a rectangle, therefore KM = BC = 7 cm, then AK = MD = (25-7) / 2 = 9 (cm). Consider a triangle CMD. In it, the angle M is straight, CD = 15 cm, then, according to the Pythagorean theorem, we find the leg CM:
CM = √ (CD ^ 2 – MD ^ 2) = √ (15 ^ 2- 9 ^ 2) = √ (225-81) = √144 = 12 (cm).
Consider a triangle AFM, in it the angle M is a straight line, AM = 25-9 = 16 (cm). By the Pythagorean theorem, we find the hypotenuse AC:
AC = √ (CM ^ 2 + AM ^ 2) = √ (12 ^ 2 + 16 ^ 2) = √ (144 + 256) = √400 = 20 (cm).