Question

8.
(diagram of two triangles, triangle abc with side ab = x - 2, ac = 5, bc (blue); triangle def with side de = x + 4, df = 15, ef (blue). below the triangles, a cross - multiplication diagram with (x - 2) connected to 15, 5 connected to (x + 4), and an equal sign. at the bottom, x = 5 is written.)

Explanation:

Step1: Set up proportion for similar triangles

Assume $\triangle ABF \sim \triangle DEF$, so $\frac{AB}{DE} = \frac{BF}{EF}$. Substitute values: $\frac{x-2}{x+4} = \frac{5}{15}$

Step2: Simplify and solve for x

Simplify $\frac{5}{15} = \frac{1}{3}$. Cross-multiply: $3(x-2) = x+4$ → $3x-6 = x+4$ → $2x=10$ → $x=5$

Answer:

5