Question

In the trapezoid at the right, BE= 2x-8, DE= x-4, and AC= x+2

A. Write and solve an equation for x

B. Find the length of each diagonal

Answer 1

A. x = 5 (Equation below)

B. AC = 9 | BD = 9

Explanation:

A. Since we know the diagonals of an isosceles trapezoid are congruent, we know that the two bottom parts of the diagonal BD (2x - 8 and x - 4) are congruent to the diagonal AC (x + 2) . This means you can just equal them together and get the value of x:

2x - 8 + x - 4 = x + 2

3x - 12 = x + 2

3x = x + 14

2x = 14

x = 7

B. Just plug in 5 for x:

AC = x + 2 = 7 + 2 = 9

BD = 2x - 8 + x -4 = 3x - 12 = 21 - 12 = 9