Pythagorean theorem - problems

Pythagorean theorem is the base for the right triangle calculator.

  1. Rectangle
    rectangle_inscribed_circle The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
  2. Square and circles
    kruznica_stvorec_1 Square with sides 41 m is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  3. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  4. Square diagonal
    square_d Calculate length of the square diagonal if the perimeter is 200 cm.
  5. Reverse Pythagorean theorem
    pytagors Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ?
  6. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  7. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  8. Isosceles right triangle
    3triangles Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
  9. 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height?
  10. Crossroads
    crossroad The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car.
  11. Floating barrel
    floating_barrel Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
  12. Rhombus 2
    koso Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
  13. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=13 cm, vb=17 cm and side b is 5 cm shorter than side a.
  14. Tank
    barrel_1 In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
  15. Hexagonal pyramid
    Hexagonal_pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
  16. Diamond
    cerveny_kosoctverec Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
  17. Above Earth
    aboveEarth To what height must a boy be raised above the earth in order to see one-fifth of its surface.
  18. Circle chord
    tetiva Determine the radius of the circle in which the chord 18 cm away from the center of the circle is 28 cm longer than the radius of the circle.
  19. Concentric circles
    chord_2 In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord.
  20. Tetrahedral pyramid
    jehlan_3 It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.

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