# Pythagorean theorem - math word problems

1. Catheti
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
2. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
3. Euclidean distance
Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
4. RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?
6. Distance
Wha is the distance between the origin and the point (18; 22)?
7. Vectors
Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
8. Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
9. Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
10. Chord - TS v2
The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
11. Diameter
If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
12. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
13. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
14. EQL triangle
15. Round table
Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
16. Trapezoid ABCD
Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
17. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector
18. Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
19. RT 10
Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
20. OPT
What is the perimeter of a right triangle with the legs 14 cm and 21 cm long?

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...

Pythagorean theorem is the base for the right triangle calculator.