Question

10. If AABC~ AEDC, find AC.

A
B
3x-5
C
5x - 5
32
56
D
E

Answer 1

AC = 70

Explanation:

given Δ ABC is similar to Δ EDC , then the ratios of corresponding sides are equal , that is

`(AC)/(EC)` =
`(BC)/(DC)` ( substitute values ) and solve for x

`(5x-5)/(56)` =
`(3x-5)/(32)` ( cross- multiply )

56(3x - 5) = 32(5x - 5) ← distribute parenthesis on both sides )

168x - 280 = 160x - 160 ( subtract 160x from both sides )

8x - 280 = - 160 ( add 280 to both sides )

8x = 120 ( divide both sides by 8 )

x = 15

Then

AC = 5x - 5 = 5(15) - 5 = 75 - 5 = 70