Answer:
The value of x = 5 answer (a)
Step-by-step explanation:
∵ There is a line parallel to the base of the Δ and intersected the other two sides formed a small Δ inside the large triangle
∴ The small Δ and the large Δ are similar
∴ Their sides are proportion
∴ [tex]\frac{x}{x+x+5}=\frac{x-2}{(x-2)(x+1)}[/tex]
∴ [tex]\frac{x}{2x+5}=\frac{x-2}{2x-1}[/tex]
∴ x(2x - 1) = (x - 2)(2x + 5)
∴ 2x² - x = 2x² + 5x - 4x -10
∴ 2x² - x = 2x² + x - 10
∴ -x - x = -10
∴ -2x = -10
∴ x = -10 ÷ -2 = 5
