# Pythagorean theorem - math word problems

1. Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
2. Regular n-gon
Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm?
3. Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
4. Right triangle eq2
Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
5. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
6. Diagonal of square
Calculate the side of a square when its diagonal is 10 cm.
7. Rhombus and diagonals
The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
8. Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
9. Two cyclists
Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start?
Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder?
11. Two diagonals
The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
12. Resultant force
Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
13. Hypotenuse
Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters.
14. Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
15. Diagonals
Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
16. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
17. Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
18. MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
19. Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
20. Plane II
A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point

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Pythagorean theorem is the base for the right triangle calculator.