Question

△ABC is similar to △LMN. Also, side AB measures 5 cm, side  AC measures 7 cm, and side  L​M measures 35 cm. What is the measure of side L​N?

Answer 1

Since triangle ABC is similar to triangle LMN, line AB is equivalent to line LM and line AC is equal to LN. SO the scale factor between lines AB and LM is 7. Line LN is 7 cm so 7 x 7= 49 cm.

Answer 2

`LN=49\ cm`

Explanation:

we know that

If triangle ABC is similar to triangle LMN

then

the ratio of their corresponding sides is equal and is called scale factor

so

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

In this problem we have

`AB=5\ cm`

`AC=7\ cm`

`LM=35\ cm`

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

Substitute the values

`(5)/(35)=(7)/(LN)`

`LN=35*7/5`

`LN=49\ cm`