Answer:
x = 40
Step-by-step explanation:
The figure shows two similar triangles. Thus, the side lengths of similar triangles are proportional to each other. Therefore:
[tex] \frac{24}{24 - 15} = \frac{x}{x - 25} [/tex]
[tex] \frac{24}{9} = \frac{x}{x - 25} [/tex]
Cross multiply
[tex] 24(x - 25) = 9(x) [/tex]
[tex] 24x - 600 = 9x [/tex]
Subtract 24x from each side
[tex] - 600 = 9x - 24x [/tex]
[tex] - 600 = -15x [/tex]
Divide both sides by -15
[tex] 40 = x [/tex]
x = 40
