Question

What is x in the similar triangles? Please help:)

Answer 1

x = 18

Explanation:

Since both right triangles are similar, therefore:

`(2x - 6)/(20) = (39)/(x + 8)`

Cross multiply

`(2x - 6)(x + 8) = 39*20`

`2x(x + 8) -6(x + 8) = 780`

`2x^2 + 16x - 6x - 48 = 780`

`2x^2 + 10x - 48 = 780`

Subtract 780 from both sides

`2x^2 + 10x - 48 - 780 = 0`

`2x^2 + 10x - 828 = 0`

`2x^2 + 46x - 36x - 828 = 0`

`2x(x + 23) - 36(x + 23) = 0`

`(x + 23)(2x - 36) = 0`

x + 23 = 0

x = -23

Or

2x - 36 = 0

2x = 36

x = 18