Question

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

Answer 1

Answer:

B. 12

Step-by-step explanation:

✔️Find the value of x

The side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

$\frac{AB}{LM} = \frac{AC}{LN}$

AB = 5

LM = 10

AC = x + 5

LN = 3x + 3

Plug in the values

$\frac{5}{10} = \frac{x + 5}{3x + 3}$

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