# Examples for 8th grade - page 5

- Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - ŽSR

Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 4-shift operation. Consider the average salary of the employee 885 €. - Rhombus ABCD

Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm. - Eiffel Tower

Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg? - Area of RT

Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 4. - Vinegar 2

How many percentage of getvinegar solution, if we mix to 2 liters of 5.9% and 2 liters of 3.5% vinegar? - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle. - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet? - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Cylinders

Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much? - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ? - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Flags

How many different flags can be made from colors purple, yellow, red, white, blue, green, orange so that each flag consisted of three different colors? - Tanks

Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr - Circle arc

Circle segment has a circumference of 41.89 m and 251.33 m^{2}area. Calculate the radius of the circle and size of central angle. - Square diagonal

Calculate length of the square diagonal if the perimeter is 476 cm. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18

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