Find the bases of a rectangular trapezoid if its large diagonal is 17 cm, its height is 8 cm

Find the bases of a rectangular trapezoid if its large diagonal is 17 cm, its height is 8 cm, and the area of the trapezoid is 100 cm2.

1. The tops of the trapezoid – A, B, C, D. BD = 17 cm. CH = 8 centimeters – height. S – area.

2. We calculate the total length of the bases of the trapezoid using the formula for calculating the area:

(BC + AD) / 2 x CH = S = 100 cm.

BC + AD = 200: 8 = 25 cm.

3. CH = AB, BC = AH, since they are the sides of the rectangle opposite each other (opposite).

4. АD = √ВD² – AB² = √289 – 64 = √225 = 15 cm.

5. BC = 25 – 15 = 10 cm.

Answer: the base of the trapezoid BC = 10 centimeters. AD = 15 centimeters.