Question

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

Answer:

The correct option is 4.

Step-by-step 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

$\frac{XC}{AC}=\frac{YC}{BC}$

$\frac{XC}{AC}=\frac{YC}{BY+YC}$

$\frac{10}{AC}=\frac{7}{4+7}$

$\frac{10}{AC}=\frac{7}{11}$

Therefore option 4 is correct.