Question

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

Answer 1

Answer:

LP = 15

Step-by-step explanation:

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

$\frac{LM}{LN}$ = $\frac{LQ}{LP}$ , substitute values

$\frac{4}{10}$ = $\frac{LQ}{LQ+QP}$

$\frac{2}{5}$ = $\frac{LQ}{LQ+9 }$ ( 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