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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

If BY 4 YC 7 XC 10 Which of the following proportions could be used to solve for AC 47 10AC 74 10AC 411 10AC 711 10AC class=

Respuesta :

StaticEntity
 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:

The correct option is 4.

Step-by-step explanation:

In triangle ABC and XYC,

[tex]\angle BAC=\angle YXC=60^{\circ}[/tex]                   (Given)

[tex]\angle BCA=\angle YCX[/tex]                                    (Reflexive Property)

By AA rule of similarity,

[tex]\triangle ABC\sim \triangle XYC[/tex]

The corresponding sides of similar triangles are proportional.

Since triangle ABC and XYC, therefore

[tex]\frac{XC}{AC}=\frac{YC}{BC}[/tex]

[tex]\frac{XC}{AC}=\frac{YC}{BY+YC}[/tex]

[tex]\frac{10}{AC}=\frac{7}{4+7}[/tex]

[tex]\frac{10}{AC}=\frac{7}{11}[/tex]

Therefore option 4 is correct.

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