The bases of an isosceles trapezoid are 56 and 104 the side is 30, find the length of the diagonal of the trapezoid.

Let’s build the height of the HВ. Since the trapezoid is isosceles, the ВH height divides the larger base into segments, the length of the smaller of which is equal to the half-difference of the base lengths.

AH = (AD – BC) / 2 = (104 – 56) / 2 = 24 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the leg BН.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 900 – 576 = 324.

BH = 18 cm.

DН = АD – АН = 104 – 24 = 80 cm.

In a right-angled triangle BDH, according to the Pythagorean theorem, BD ^ 2 = DH ^ 2 + BH ^ 2 = 6400 + 324 = 6724.

ВD = 82 cm.

Answer: The length of the diagonal is 82 cm.