# Pythagorean theorem - math word problems

1. Isosceles trapezoid
The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
2. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
3. Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
4. Rectangular trapezoid
The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
5. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?
7. Rectangular garden
The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
8. Right 24
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
9. Right isosceles triangle
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
10. The garden
The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?
11. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
12. On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
13. Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
14. Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
15. Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
16. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
17. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
18. AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
19. Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
20. The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motio

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Pythagorean theorem is the base for the right triangle calculator.