# 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 result:

x =  0.354 cm

#### Solution:

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

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Square diagonal
Calculate the length of diagonal of the square with side a = 23 cm.
• Tree trunk
From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
• Calculation
How much is sum of square root of six and the square root of 225?
The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
• Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
• Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
• Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
• Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
• Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
• Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
• Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6