# Examples for secondary school students - page 62

- Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Tractors

Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately? - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Fruit tea

Tea contains 7% of fruit components and 12% of sugar in this component. How many percents of sugar is represented in the whole tea? - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Cube, cuboid, and sphere

Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere? - The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Endless lego set

The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They - Dice

We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times? - Linear imaginary equation

Given that ? "this is z star" Find the value of the complex number z. - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Candy and boxes

We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of. - Mean

A student food the mean of 50 items as 38.6. When checking the work he found that he had taken one item as 50 why it should correctly read as 40 in this circumstances. What should be the correct mean? - Speed of car

The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed. - Largest angle of the triangle

Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a - Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Saving 9

An amount if $ 2000 is invested at an interest of 5% per month. if $ 200 is added at the beginning of each successive month but no withdrawals. Give an expression for the value accumulated after n months. After how many months will the amount have accumula - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a

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