Question

Can someone help me on this question and explain the process?

Solve for x. The triangles in each pair are similar.

Answer 1

x = 10

Explanation:

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

`(TS)/(TB)` =
`(TR)/(TC)` ( substitute values )

`(10x+17)/(65)` =
`(90)/(50)` ( cross- multiply )

50(10x + 17) = 90 × 65 = 5850 ( divide both sides by 50 )

10x + 17 = 117 ( subtract 17 from both sides )

10x = 100 ( divide both sides by 10 )

x = 10