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 the length of DC

In right - triangle BDC, using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here, \(a = 24\), \(c = 25\), and we want to find \(b=DC\).

$$DC=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}=\sqrt{49}=7$$

Step2: Find the length of EC

Since ABDE is a rectangle, \(ED=AB = 20\). Then \(EC=ED + DC=20+7 = 27\)

Step3: Calculate the perimeter of trapezoid ABCE

The perimeter \(P=AB + BC+CE+EA\). We know \(AB = 20\), \(BC = 25\), \(CE=27\), \(EA = 24\)

$$P=20 + 25+27+24=96$$

Answer:

D. 96 units