Question

select the correct answers. line segment bd divides trapezoid abce into a rectangle and a right triangle as shown. what is the perimeter of the trapezoid? a 20 b 24 e d c a. 49 units b. 69 units c. 76 units d. 96 units e. 133 units

Explanation:

Step1: Find length of ED

Since ABDE is a rectangle, ED = AB = 20.

Step2: Find length of EC

In right - triangle BDC, using the Pythagorean theorem to find DC. Let BD = 24 and BC = 25. Then $DC=\sqrt{BC^{2}-BD^{2}}=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}=\sqrt{49}=7$. So EC=ED + DC=20 + 7 = 27.

Step3: Calculate the perimeter of trapezoid

The perimeter of trapezoid ABCE is AB+BC + CE+EA. AB = 20, BC = 25, CE = 27, EA = 24. So the perimeter is 20+25 + 27+24=96.

Answer:

D. 96 units