# Units - math word problems

1. Is right-angled Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle?
2. Clouds Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
3. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
4. Water block A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
5. Diamond The diamond has a circumference of 48cm. Calculate the length of its side in dm.
6. Scale factor A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
7. Unit rate Find unit rate: 6,840 customers in 45 days
8. Train delay The train should be in the station for 10 minutes. It still has 32 km left. What is the expected delay if the train travels in 2 minutes 3 km except for the last section where it is 2 km in 5 minutes.
9. Garden The garden around the new majer is divided as follows: 35% vegetable, 30% fruit orchards, 10% flowers and the remaining 120 m2 are lawns. What is the total area of the garden?
10. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
11. Percentages What is 1/3 of \$821.43? Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters?
13. Display case Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
14. Farmland Farmers seeded maize to 45 ha, which is 15% of their total farmland. How many hectares of fields they have?
15. Thales Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
16. Garden fence The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
17. Two brothers The two brothers were to be divided according to the will of land at an area of 1ha 86a 30m2 in a ratio of 5:4. How many will everyone get?
18. Five mechanics Five mechanics will make a car for some time. How many cars can 30 mechanics produce at the same time?
19. Tea mixture Of the two sort of tea at a price of 180 CZK/kg and 240 CZK/kg we make a mixture 12 kg that should be prepared at a price of 200 CZK / kg. How many kilos of each sort of tea will we need to be mixed?
20. Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm

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