# Pythagorean theorem - problems

Pythagorean theorem is the base for the right triangle calculator.- Square and circles

Square with sides 82 km is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Rectangle

The rectangle is 36 cm long and 48 cm wide. Determine the radius of the circle circumscribing rectangle. - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Reverse Pythagorean theorem

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 ? - Rhombus

It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 6 cm and a_{2}= 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height? - Crossroads

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. - 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. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Tank

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? - 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. - Diamond

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. - Circle chord

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. - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - Concentric circles

In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord. - Tetrahedral pyramid

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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