# Length - 9th grade (14y) - math problems

1. The escalator I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I climb
2. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
3. Uphill garden I have a garden uphill, increasing from 0 to 4.5 m for a length of 25 m, how much is the climb in percent?
4. Land boundary The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
5. AMSL and skiing Tomas skis from point A (3200m above sea level to place B. Hill has 20% descent. The horizontal distance between the start and finish is 2,5km. At what altitude is point B?
6. Parallels and one secant There are two different parallel lines a, b and a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
7. Distance between 2 points Find the distance between the points (7, -9), (-1, -9)
8. 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?
9. Gutter pipe How many m² of sheet metal is required to produce a 12 m long and 18 cm wide gutter, if 7% bend is required?
10. Sand castle Tim and Tom built a sand castle and embellished it with a flag. Half the pole with the flag plunged into the castle. The highest point of the pole was 80 cm above the ground, its lowest point 20 cm above the ground. How high was the sand castle?
11. 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?
12. Wave parameters Calculate the speed of a wave if the frequency is 336 Hz and the wavelength is 10 m.
13. Cheetah vs antelope When the cheetah began chasing the antelope, the distance between them was 120 meters. Although the antelope was running at 72km/h, the cheetah caught up with it in 12 seconds. What speed was the cheetah running?
14. Bike ride Marek rode a bike ride. In an hour, John followed him on the same route by car, at an average speed of 72 km/h, and in 20 minutes he drove him. Will he determine the length of the way that Marek took before John caught up with him, and at what speed did Ma 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?
16. Cable car Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
17. Rocket start The body launched vertically up returns to the start site in 6 seconds. What height did it have?
18. Four poplars Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
19. The mast The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
20. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.

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