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

Question

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

falling_in_katt · Answer

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

anonymous · Answer

|dw:1435253142857:dw|

mathstudent55 · Answer

|dw:1435253385372:dw|

mathstudent55 · Answer

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

mathstudent55 · Answer

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.

mathstudent55 · Answer

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

falling_in_katt · Answer

$$3\sqrt{2}$$

mathstudent55 · Answer

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