Ratio + expression of a variable from formula - math problems

On solving problems and tasks with proportionally we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members makes possible to calculate the fourth - unknown member.

1. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
2. Right triangle Legs of right are in ratio a:b = 2:8. Hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
3. ISO triangle Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
4. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
5. Pumps Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
6. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
7. Trapezoid Area of trapezoid is 135 cm2. Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
8. RT and ratio A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
9. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
10. Similarity of squares The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
12. Painting rooms If Dano paint three hours daily given work he complete in 7.5 days. How many hours a day would have to work to finish the job 1.5 days earlier?
13. Rhombus and diagonals The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
14. Divide money 2 Ben and Dan had the same amount of money at the start. When Ben gave 300 to Dan, the ratio of Ben 's money to Dan's money became 2:3. How much money did each have at first?
15. Isosceles trapezoid Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week?
17. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
18. Rectangle Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height)
19. Rectangle 3-4-5 The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
20. Cuboid - edges The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid

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