Question

Help me with this question...

Answer 1

Answer:

Option D

Step-by-step explanation:

Since, $\frac{x-y}{x+y}=\frac{2}{7}$

7(x - y) = 2(x + y)

7x - 7y = 2x + 2y

7x - 2x = 2y + 7y

5x = 9y

$\frac{x}{y}=\frac{9}{5}$

Since, ΔAED is similar to ΔACB,

Corresponding sides of these triangles will be proportional.

$\frac{BC}{DE}=\frac{AC}{AE}$

$\frac{x}{y}=\frac{8+AE}{AE}$

$\frac{9}{5} =\frac{8+AE}{AE}$

9(AE) = 40 + 5AE

9(AE) - 5(AE) = 40

4(AE) = 40

AE = 10 cm

Therefore, Option D will be the answer.