## Falling_In_Katt one year ago In triangle RST, XY is parallel to RS. If TX = 3, XR = TY, and YS = 6, find XR.

1. Falling_In_Katt

A.$3\sqrt{3}$ B. $4\sqrt{3}$ C.$\sqrt{5}$ D.$3\sqrt{2}$

2. anonymous

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3. mathstudent55

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4. mathstudent55

Call the two congruent unknown segments x. |dw:1435253471031:dw|

5. mathstudent55

When you draw a segment parallel to a side of a triangle, it divides the sides of the triangles into proportional segments. Use the proportion that @nitishdua31 wrote above, using x where necessary.

6. mathstudent55

$$\dfrac{TX}{TR} = \dfrac{TY}{TS}$$ $$\dfrac{3}{x + 3} = \dfrac{x}{x + 6}$$

7. Falling_In_Katt

$3\sqrt{2}$

8. mathstudent55

$$\dfrac{3}{x + 3} = \dfrac{x}{x + 6}$$ $$x(x + 3) = 3(x + 6)$$ $$x^2 + 3x = 3x + 18$$ $$x^2 = 18$$ $$x = \sqrt {18}$$ $$x = 3\sqrt 2$$ You are correct.