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 25 e d c a. 49 units b. 69 units c. 76 units d. 96 units e. 133 units

Explanation:

Step1: Find length of DC

In right - triangle BDC, using the Pythagorean theorem. Let \(BD = 24\) (height of the rectangle and triangle) and \(BC = 25\). By \(a^{2}+b^{2}=c^{2}\), where \(c = BC\), \(a = BD\), and \(b = DC\). So \(DC=\sqrt{BC^{2}-BD^{2}}=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}=\sqrt{49\times1}=7\).

Step2: Identify lengths of other sides

Since ABDE is a rectangle, \(AB = 20\), \(AE=BD = 24\), and \(ED = AB = 20\).

Step3: Calculate perimeter of trapezoid

Perimeter of trapezoid \(ABCE=AB + BC+CE + AE\). \(CE=ED + DC=20 + 7=27\). So perimeter \(=20+25 + 27+24=96\).

Answer:

D. 96 units