Question

In each of the following, solve for X.

Answer 1

x = 6

Explanation:

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

`(MO)/(PR)` =
`(MN)/(PQ)` ( substitute values )

`(4+x)/(5)` =
`(x-2)/(2)` ( cross- multiply )

5(x - 2) = 2(4 + x) ← distribute parenthesis on both sides

5x - 10 = 8 + 2x ( subtract 2x from both sides )

3x - 10 = 8 ( add 10 to both sides )

3x = 18 ( divide both sides by 3 )

x = 6