Question

In triangle RST,
If TX = 3, XR = TY, and
YS = 6, find XR.

Answer 1

x = 3√2  is what i got

Answer 2

Answer:

$XR=3\sqrt{2}\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The triangle RST and the triangle XYT are similar

then

the ratio of their corresponding sides are equal  

$\frac{XT}{TR}=\frac{TY}{TS}$

substitute the values

$\frac{3}{a+3}=\frac{a}{a+6}$

$3(a+6)=a(a+3)\\3a+18=a^{2} +3a\\ a^{2}=18\\a=3\sqrt{2}\ units$

$XR=3\sqrt{2}\ units$