Question

If triangle LMQ is similar to triangle LNP, calculate the length of segment LP.

Answer 1

LP = 15

Explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

`(LM)/(LN)` =
`(LQ)/(LP)` , substitute values

`(4)/(10)` =
`(LQ)/(LQ+QP)`

`(2)/(5)` =
`(LQ)/(LQ+9 )` ( cross- multiply )

5LQ = 2(LQ + 9) = 2LQ + 18 ( subtract 2LQ from both sides )

3LQ = 18 ( divide both sides by 3 )

LQ = 6

Then

LP = LQ + QP = 6 + 9 = 15