Question

For the pair of similar triangles, find the value of x.

2x8
x+8
24
The value of x is a
(Simplify your answer. Use a comma to separate answers as needed.)

Answer 1

Answer: x = 22

Explanation:

Compare the 2 triangles

`(2x-8)/(24) = (45)/(x+8)`

Cross multiply

(2x-8) (x+8) = 45 x 24

2x^2 + 16x - 8x - 64 = 1080

2x^2 + 8x - 64 - 1080 = 0

2x^2 + 8x - 1144 = 0 ---> divide by 2

x^2 + 4x - 572 = 0

(sum and product)

x^2 - 22x + 26x - 572 = 0

x(x - 22) + 26(x - 22) = 0

(x + 26) (x - 22) = 0

x + 26 = 0

x = -26

x - 22 = 0

x = 22