ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?

Final Answer:

x =  0.3536 cm

Step-by-step explanation:

$$\begin{gathered} a=1\text{cm} \\ u=\sqrt{2}\cdot a=\sqrt{2}\cdot 1=\sqrt{2}\text{cm}\doteq 1.4142\text{cm} \\ {u}_1=3/4\cdot u=3/4\cdot 1.4142\doteq 1.0607\text{cm} \\ {u}_2=1/4\cdot u=1/4\cdot 1.4142\doteq 0.3536\text{cm} \\ {u}_3=3/4\cdot a=3/4\cdot 1=\frac{3}{4}=0.75\text{cm} \\ {u}_4=1/4\cdot a=1/4\cdot 1=\frac{1}{4}=0.25\text{cm} \\ s=a/2=1/2=\frac{1}{2}=0.5\text{cm} \\ {s}_2=s-u_4=0.5-0.25=\frac{1}{4}=0.25\text{cm} \\ x=\sqrt{s_2^2+u_4^2}=\sqrt{0.25^2+0.25^2}=0.3536\text{cm} \end{gathered}$$

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