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:

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

Try another example

Related math problems and questions:

• Triangle in a square
  In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
• Diagonals
  Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
• A rectangle 2
  A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
• Square diagonal
  Calculate the length of the square diagonal if the perimeter is 172 cm.
• Square diagonal
  Calculate the length of diagonal of the square with side a = 11 cm.
• IS trapezoid
  Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
• Find the
  Find the length of the side of the square ABCD, which is described by a circle k with a radius of 10 cm.
• Square ABCD
  Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
• Body diagonal
  Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
• Two diagonals
  The rhombus has a side length of 12 cm and a length of one diagonal of 21 cm. What is the length of the second diagonal?
• Trapezoid thirds
  The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
• Circle and square
  An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
• Chord
  It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
• Diagonal
  The rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has an area of 15 cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
• Diagonal BD
  Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42°
• Rectangle diagonals
  It is given a rectangle with an area of 24 cm² a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.