# Pythagorean theorem - math word problems

1. Circle chord
Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle.
2. Windbreak
A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
3. Embankment
Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
4. Kite
John a kite, which is diamond shaped. Its diagonals are 60 cm long and 90 cm long. Calculate: a) the diamond side b) how much paper John needs to make a kite if he needs paper on both sides and needs 5% of the paper for bending.
5. Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
6. Chord 5
It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
7. Semicircle
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
8. Points on circle
In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
9. 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.
10. Diamond perimeter
Calculate the diamond circumference which area is 288 cm square and one diagonal has a size of 124 cm.
11. Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
12. Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
13. 3s prism
It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
14. Is right?
Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
15. Isosceles trapezoid
Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
16. Two aircraft
Two planes fly to the airport. At some point, the first airplane is away from the airport 98 km and the second 138 km. The first aircraft flies at an average speed of 420 km/h, the second average speed is 360 km/h, while the tracks of both planes are perp
17. Dig water well
Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?
18. Stairway
Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
19. The cellar
Mr Novák has a cellar and a cellar window in the chalet has 0.6 meter square window. The window wishes to place an X-shaped grid in a square. He uses iron welded bars. Calculate the lengths of individual bars and what the total length of the bars he has
The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.

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Pythagorean theorem is the base for the right triangle calculator.