# 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?

Result

x =  0.354 cm

#### Solution:

$a=1 \ \text{cm} \ \\ u=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 1 \doteq \sqrt{ 2 } \ \text{cm} \doteq 1.4142 \ \text{cm} \ \\ \ \\ u_{ 1 }=3/4 \cdot \ u=3/4 \cdot \ 1.4142 \doteq 1.0607 \ \text{cm} \ \\ u_{ 2 }=1/4 \cdot \ u=1/4 \cdot \ 1.4142 \doteq 0.3536 \ \text{cm} \ \\ \ \\ u_{ 3 }=3/4 \cdot \ a=3/4 \cdot \ 1=\dfrac{ 3 }{ 4 }=0.75 \ \text{cm} \ \\ u_{ 4 }=1/4 \cdot \ a=1/4 \cdot \ 1=\dfrac{ 1 }{ 4 }=0.25 \ \text{cm} \ \\ \ \\ s=a/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \text{cm} \ \\ \ \\ s_{ 2 }=s - u_{ 4 }=0.5 - 0.25=\dfrac{ 1 }{ 4 }=0.25 \ \text{cm} \ \\ \ \\ x=\sqrt{ s_{ 2 }^2 + u_{ 4 }^2 }=\sqrt{ 0.25^2 + 0.25^2 } \doteq 0.3536 \doteq 0.354 \ \text{cm}$

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