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?

Correct answer:

x =  0.3536 cm

Step-by-step explanation:

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

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