# Length - math word problems

1. Velocipedes In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, wh
2. Poplar How tall is a poplar by the river, if we know that 1/5 of its total height is a trunk, 1/10th of the height is the root and 35m from the trunk to the top of the poplar?
3. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
4. Average height The average height of all pupils is 162 cm. The class teacher's height is 178 cm. The average height of all (teacher and all pupils) is 163 cm. Calculate the number of pupils in the class.
5. Constant motion The car has undergone constant motion 120 km in 1 hour 30 minutes. Determine its average speed. Determine how long car drove in the first 20 minutes and 50 minutes from the start of the move.
6. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
7. Wave parameters Calculate the speed of a wave if the frequency is 336 Hz and the wavelength is 10 m. Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
9. Isosceles triangle In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
10. Diameter of a cylinder The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
11. Two gears The two gears fit together. The larger gear has 32 teeth, the smaller has 20 teeth less. How many times does turn a smaller gear if the bigger gear turns three times?
12. Grandmother Mom walked out to visit her grandmother in a neighboring village 5km away and moved at a speed of 4km/h. An hour later, father drove down the same road at an average speed of 64km/h. 1) How long will take to catch mom die? 2) What is the approximate di
13. The rod The rod has a length of 90cm. Half is painted blue, the third is red and the rest is yellow. How long is the yellow part of the rod?
14. Two cyclists 2 At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min, 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.
16. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
17. 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
18. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
19. Two cities The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
20. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.

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