Question

If BY = 4, YC = 7, XC = 10. Which of the following proportions could be used to solve for AC?

4/7 = 10/AC
7/4 = 10/AC
4/11 = 10/AC
7/11 = 10/AC

Answer 1

line XY goes in through triangle ABC, and Y lies between lines BC while X lies between lines AC
The ratio of similar sides to triangles should be equal AC/XC=BC/YC BC=BY+YC BC=4+7=11
AC/10=11/7 or 7/11=10/AC the ratio above should be used for calculation of AC

Answer 2

The correct option is 4.

Explanation:

In triangle ABC and XYC,

`\angle BAC=\angle YXC=60^(\circ)` (Given)

`\angle BCA=\angle YCX` (Reflexive Property)

By AA rule of similarity,

`\triangle ABC\sim \triangle XYC`

The corresponding sides of similar triangles are proportional.

Since triangle ABC and XYC, therefore

`(XC)/(AC)=(YC)/(BC)`

`(XC)/(AC)=(YC)/(BY+YC)`

`(10)/(AC)=(7)/(4+7)`

`(10)/(AC)=(7)/(11)`

Therefore option 4 is correct.