# Examples for 9th grade - page 89

- Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Three pumps

We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump? - Enlarged rectangle

The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle? - Father and sons

After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now? - Square prism

Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms. - Two cities

The distance between cities A and B is 132 km. At 9.00 am, the cyclist started the bike at an average speed of 24 km/h, and at 10.00 h started from the B cyclist at an average speed of 30 km/h. How long and far from A will they both meet? - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - Fruit juice

Fruit juice contains 37.5% sugar. How many percents of sugar will be in the flavored mineral that we prepare from 100 grams of fruit juice and 1.4 liters of mineral? (1 liter = 1 kg) - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm^{2}. What dimensions can this large rectangle have? Write all options. Explain your calcu - Minimum surface

Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed. - Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste. - Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm. - Viju

viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with viju?? - The coil

How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm - Work

The first worker would need less than 4 hours to complete the task than the other worker. In fact, both workers worked for two hours together, then the first worker did the remaining work himself. In what proportion should the remuneration of the workers b - Spending

If spends 25% of my net pay of $922.28 on entertainment. How much money is that? - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - 7 digit number

If 3c54d10 is divisible by 330, what is the sum of c and d? - Big cube

Calculate the surface of the cube, which is composed of 64 small cubes with an edge 1 cm long. - Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.

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