Answer:
Option D
Step-by-step explanation:
Since, [tex]\frac{x-y}{x+y}=\frac{2}{7}[/tex]
7(x - y) = 2(x + y)
7x - 7y = 2x + 2y
7x - 2x = 2y + 7y
5x = 9y
[tex]\frac{x}{y}=\frac{9}{5}[/tex]
Since, ΔAED is similar to ΔACB,
Corresponding sides of these triangles will be proportional.
[tex]\frac{BC}{DE}=\frac{AC}{AE}[/tex]
[tex]\frac{x}{y}=\frac{8+AE}{AE}[/tex]
[tex]\frac{9}{5} =\frac{8+AE}{AE}[/tex]
9(AE) = 40 + 5AE
9(AE) - 5(AE) = 40
4(AE) = 40
AE = 10 cm
Therefore, Option D will be the answer.
