Question

Line segment BD divides trapezoid ABCE into a rectangle and a right triangle as shown. What is the perimeter of the trapezoid?

Answer 1

Answer:

$\left[\begin{array}{ccc}A&49\\B&69&CorrectAnswer\\C&76\\D&96\\E&133\end{array}\right]$

$\left[\begin{array}{ccc}Find&The&Perimeter\end{array}\right]$

$Add$$The$$Lengths$$Of$$All$$4$$sides$

Answer 2

The perimeter of trapezoid ABCE = AB + BC + DC + ED + AE = 96 units.

What is the Perimeter of a Trapezoid?

The perimeter of a trapezoid = sum of all its sides.

Given the following lengths of the trapezoid:

• AE = BD = 24
• AB = ED = 20
• BC = 25
• DC = ?

Find DC using the Pythagorean theorem:

DC = √(BC² - BD²)

Substitute

DC = √(25² - 24²)

DC = 7 units

Perimeter of trapezoid ABCE = AB + BC + DC + ED + AE = 20 + 25 + 7 + 20 + 24

Perimeter of trapezoid ABCE = 96 units.

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