The smaller base of the rectangular trapezoid is 9cm, the large diagonal is 17cm

The smaller base of the rectangular trapezoid is 9cm, the large diagonal is 17cm, and the height is 8cm. Find the perimeter of the trapezoid.

1. The tops of the trapezoid – A, B, C, D. CH = 8 centimeters – height. BD = 17 centimeters – diagonal. BC = 9 centimeters. P is the perimeter.

2. Calculate the length of the larger base using the Pythagorean theorem:

AD = √BD² – AB² = √17² – 8² = √289 – 64 = √225 = 15 centimeters.

3. DH = AD – AH. AH = BC.

DH = 15 – 9 = 6 centimeters.

4. Calculate the length of the CD side:

CD = √CH² + DH² = √8² + 6² = √64 + 36 = √100 = 10 centimeters.

5.P = AB + CD + BC + AD = 8 + 10 + 9 + 15 = 42 centimeters.