Question

Can someone help me solve for x and y of this?

Answer 1

x = 10

y = 5

Explanation:

Since, two lines p and q are the parallel lines and FA is a transversal line intersecting these parallel lines.

ΔAOB and ΔDOC are the similar triangles.

Therefore, by the property of similar triangles, corresponding sides of the similar triangles will be proportional.

`(AO)/(OD)= (OB)/(OC)`

`(x)/(15)= (8)/(12)`

x =
`(15* 8)/(12)`

x = 10

Similarly, triangles AOB and OEF will be similar.

And by the property of similar triangles,

`(AO)/(OF)= (OB)/(OE)`

`(x)/(15+y)= (8)/(12+4)`

`(10)/(15+y)= (8)/(16)`

8(15 + y) = 160

120 + 8y = 160

8y = 160 - 120

8y = 40

y = 5