Question

If BCF ~ BDE, solve for x

Answer 1

x = 10

Explanation:

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

`(BE)/(BF)` =
`(BD)/(BC)` ( substitute values )

`(56+5x-8)/(56)` =
`(52+39)/(52)` , that is

`(48+5x)/(56)` =
`(91)/(52)` ( cross- multiply )

52(48 + 5x) = 56 × 91 = 5096 ( divide both sides by 52 )

48 + 5x = 98 ( subtract 48 from both sides )

5x = 50 ( divide both sides by 5 )

x = 10