# Ratio + length - 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 make possible to calculate the fourth - unknown member.

1. Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
2. Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if at the same time a column 2.5 m high has a shadow of 1.5 m.
3. Squares ratio
The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
4. Marlon
Marlon drew a scale drawing of a summer camp. In real life, the sand volleyball court is 8 meters wide. It is 4 centimeters wide in the drawing. What is the drawing's scale factor? Simplify your answer and write it as a ratio, using a colon.
5. Altitude difference
What a climb in per mille of the hill long 4 km and the altitude difference is 6 meters?
6. Two trains
Two trains departed from City A and City B against each other. They met after some time. The first train then took 9 hours to reach city B, and the second train took 4 hours to reach city A. In what proportion were the train speeds?
7. 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?
8. Two villages
On the map with a scale of 1:40000 are drawn two villages actually 16 km away. What is their distance on the map?
9. The perimeter 3
The perimeter of a rectangle is 35 cm. The ratio of the length to its width is 3:2. Calculate the dimensions of the rectangle
10. Tourist
A tourist walked an average speed of 3.5 km/h route in 6 hours. Calculate how many hours he would have passed at an average speed of 5.5 km/h.
11. Geometric plan
At what scale the building plan if one side of the building is 45m long and 12mm long on a plan?
12. Lighthouse
Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea
13. 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?
14. The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
15. Scale of the map
The distance between two cities is actually 30 km and the map is 6 cm. What is the scale of the map?
16. Points on line segment
Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
17. 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.
18. Photocopier
A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
19. 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.
20. Photo egative
Negative dimensions are 36mm and 28mm. What will be the photo size in the 21:4 ratio?

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