Question

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

Answer 1

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

Answer 2

Call the two congruent unknown segments x.

Answer 3

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.

Answer 4

\(\dfrac{TX}{TR} = \dfrac{TY}{TS}\)

\(\dfrac{3}{x + 3} = \dfrac{x}{x + 6} \)

Answer 5

\[3\sqrt{2}\]

Answer 6

\(\dfrac{3}{x + 3} = \dfrac{x}{x + 6}\)

\(x(x + 3) = 3(x + 6) \)

\(x^2 + 3x = 3x + 18\)

\(x^2 = 18\)

\(x = \sqrt {18}\)

\(x = 3\sqrt 2\)

You are correct.