Question

Help me with this question...

Answer 1

Option D

Explanation:

Since,
`(x-y)/(x+y)=(2)/(7)`

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

7x - 7y = 2x + 2y

7x - 2x = 2y + 7y

5x = 9y

`(x)/(y)=(9)/(5)`

Since, ΔAED is similar to ΔACB,

Corresponding sides of these triangles will be proportional.

`(BC)/(DE)=(AC)/(AE)`

`(x)/(y)=(8+AE)/(AE)`

`(9)/(5) =(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.