Question

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

Answer 1

Answer:

x = 18

Step-by-step explanation:

Since both right triangles are similar, therefore:

$\frac{2x - 6}{20} = \frac{39}{x + 8}$

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