Ratio - 9th grade (14y) - examples - page 6
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.
- Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
- Smallest internal angle
Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
Sprinter runs the relay 4 x 400 m to the handover at speed 42 km/h. A second runner is at the start of the handover area 20 m long and runs when it is the first sprinter at distance 10 m. Calculate the speed at which the second runner must run in order to.
- Line segment
For the line segment whose endpoints are L[-9, 4] and M[-18, 14], find the x and y value for the point located 4 over 6 the distance from L to M.
- Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
- Middle segment
In a triangle ABC with the side /AB/ = 24 cm is constructed middle segment /DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
- Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?
- V - slope
The slope of the line whose equation is -3x -9 = 0 is
The speedometer of a car reads 66 km/h. It's accurate to within 4.1% What is the maximum possible error?
We burned two unequally thick and long candles. Longer burnt for three and a half hours and shorter for five hours. After two hours of burning it was identical. How many times was longer candle longer then shorter?
- Volume of three cuboids
Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
- Seven tractors
Seven tractor plowed 308 ha field in four days. How many hectares of fields will plowe 9 tractors in 3 days at the same power?
- 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.
- Basic form
Expressed the ratios of values in the basic form: 0,5 t : 1,2 kg 200 l : 0,15 m3 12 t : 3600 kg 500 kg : 2,5 t 0,9 kg : 500 g 3,6 m : 240 cm 1200 mm : 2,4 m 300 l : 0,3 m3 6 min 30 s : 900 s
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?
- Three co-owners
The three co-owners of building company have earnings from a contract portioned in the ratio of 3:6:7. Each of them received the amount in whole USD. One of them on contract earned 86450 USD. What was the total earnings this order?
- Tree shadow
The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
- 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.
- Mason with assistant
Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work?
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