Pythagorean theorem - math word problems - page 24

1. Construct Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
2. 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?
3. 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
4. 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].
5. 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. 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.
7. Prism 4 sides The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
8. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
9. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. 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?
11. Body diagonal Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonal.
12. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
13. 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.
14. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.
15. Isosceles triangle The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z.
16. Right angled triangle 3 Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
17. Rectangle There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
18. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
19. 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.
20. 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?

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Pythagorean theorem is the base for the right triangle calculator.