# Pythagorean theorem - examples - page 24

1. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
2. Is right-angled
Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle?
3. Find radius
Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
4. Construct
Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
5. Cone 15
The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
6. 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
7. 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.
8. Pendulum
Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
9. Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
10. Body diagonal - cube
Calculate the surface and cube volume with body diagonal 15 cm long.
11. Quadrangular pyramid
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.
12. Cross road
From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes?
13. Vertices of a right triangle
Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
14. Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
15. Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
16. Slant height
The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
17. Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
18. Isosceles triangle
The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
19. Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees
20. Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.

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Pythagorean theorem is the base for the right triangle calculator.