Examples for 9th grade - page 21

  1. Right triangle
    thales_2 Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
  2. Dog
    dog_and_man Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination?
  3. Isosceles III
    demos The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
  4. Rectangle
    obdlznik_torta Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
  5. Equilateral cylinder
    3d Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
  6. Cuboid
    cuboid_3 Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
  7. Bits, bytes
    bits Calculate how many different numbers can be encoded in 16-bit binary word?
  8. Tetrahedral prism
    hranol4sreg Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
  9. Party
    party-informatikov At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party?
  10. Horizon
    lighthouse The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
  11. Kids
    kids How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
  12. Boat
    boat_ramp A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
  13. Perpendicular
    slopeplane What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?
  14. Similarity n-gon
    podobnost 9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S1=190 dm2 and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.
  15. Geometric mean
    geom_mean Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
  16. Rectangle
    rectangles_1 The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
  17. Oil rig
    oil_rig_tower Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
  18. Two runners
    sprinters_1 Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
  19. Tiles
    dlazdice From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
  20. Baker
    pekar The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?

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



To this e-mail address, we will reply solution; 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...