Square diagonal

Calculate the length of diagonal of the square with side a = 23 cm.


Correct result:

d =  32.53 cm

Solution:

a=23 cm  d2=a2+a2=232+232=1058 d=2⋅ a=2⋅ 23=23 2=32.53 cma=23 \ \text{cm} \ \\ \ \\ d^2=a^2 + a^2=23^2 + 23^2=1058 \ \\ d=\sqrt{ 2 } \cdot \ a=\sqrt{ 2 } \cdot \ 23=23 \ \sqrt{ 2 }=32.53 \ \text{cm}

Try another example


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!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 2 comments:
#
Math student
Why do you need to do
d squared = a squared + a squared

#
Dr Math
just  simple Pythagorean therorem

avatar






Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric 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: video1   video2

Next similar math problems:

  • Tree trunk
    tram 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.
  • Two circles
    intersect_circles Two circles with the same radius r = 1 are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles?
  • Sum of squares
    pytagorean The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
  • Broken tree
    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?
  • The ladder
    rebrik33_1 The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
  • Diagonals in diamons/rhombus
    diamonds Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal.
  • Park
    diamond_3 In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
  • Satin
    diagonal_rectangle_3 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?
  • Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  • The right triangle
    rt_tr540 The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
  • Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  • Isosceles trapezoid
    lichobeznik_mo_z8_5 What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
  • A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  • Holidays - on pool
    pool_4 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?
  • Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  • Double ladder
    rr_rebrik The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
  • Double ladder
    dvojak The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?