# Pythagorean theorem - math word problems

1. KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
2. Tetrahedral pyramid
Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
3. Rectangular field
A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
4. Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor an
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
6. Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
7. Cuboidal room
Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
8. Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
9. Circle described
The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
10. Infinite sum of areas
Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
11. Octagonal tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
12. Find diagonal
Find diagonal of cuboid with length=20m width=25m height=150m
13. Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
14. Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
15. Waste
How many percents are waste from a circular plate with a radius of 1 m from which we cut a square with the highest area?
16. Diagonals of a rhombus 2
One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
17. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
18. Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
19. Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
20. Diagonals of the rhombus
How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm2?

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Pythagorean theorem is the base for the right triangle calculator.