# Pythagorean theorem - math word problems

1. Rectangle The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
2. Tiles How much you will pay CZK for laying tiles in a square room with a diagonal of 8 m if 1 m2 cost CZK 420?
3. Rectangle - desc circle Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.
4. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
5. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area?
6. Area of the cone Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
7. Cube from sphere What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
8. Chord distance The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
9. Hexagonal pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
10. Moivre 2 Find the cube roots of 125(cos 288° + i sin 288°). Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ. An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
13. Chord 4 I need to calculate the circumference of a circle, I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle. A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
15. Chord AB What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
16. Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
17. Rectangle and circle The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
18. Two forces Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
19. Silver medal To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
20. RTriangle 17 The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.

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Pythagorean theorem is the base for the right triangle calculator.