Question

Given that ABC~LMN
What is the length of AC?

Answer 1

B. 12

Explanation:

✔️Find the value of x

The side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

`(AB)/(LM) = (AC)/(LN)`

AB = 5

LM = 10

AC = x + 5

LN = 3x + 3

Plug in the values

`(5)/(10) = (x + 5)/(3x + 3)`

Cross multiply

`5(3x + 3) = 10(x + 5)`

`15x + 15 = 10x + 50` (distributive property)

Collect like terms

`15x - 10x = -15 + 50`

`5x = 35`

Divide both sides by 5

x = 7

✔️Find AC

AC = x + 5

Plug in the value of x

AC = 7 + 5

AC = 12