Answer: x = 22
Step-by-step explanation:
Compare the 2 triangles
[tex]\frac{2x-8}{24} = \frac{45}{x+8}[/tex]
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
