Question

If ABE is similar to ACD what is the value of AB

Answer 1

AB corresponds to AC. Both are the left diagonal lines of triangle ABE and triangle ACD. Both AB and AC are also the first two letters of ABE and ACD respectively

BE and CD correspond as well. They are the horizontal sides of the two triangles. BE and CD are the last two letters of ABE and ACD.

Set up the proportion below. Then solve for x

AB/AC = BE/CD

AB/(AB+BC) = BE/CD

x/(x+3) = 2/5

5x = 2(x+3)

5x = 2x+6

5x-2x = 6

3x = 6

x = 2

Answer: AB = 2

note how AB = x = 2, so AC = AB+BC = x+3 = 2+3 = 5. This forms the ratio AB/AC = 2/5 which is identical to the ratio BE/CD = 2/5