# Examples for 8th grade - page 5

- Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm. - Square and circles

Square with sides 41 m is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Rectangle

In rectangle with sides 10 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Two cars

Two cars started against each other at the same time to journey long 225 km. First car went 35 km/h and second 48 km/h. What distance will be between this cars 20 minutes before meet? - Area of RT

Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15. - 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 4.8 kg? - Proof PT

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

In the yard were chickens and rabbits. They had 44 heads and 124 legs. How many chickens and how many rabbits was in the yard? - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 17 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - No. of divisors

How many different divisors has number ?? - Tanks

Fire tank has cuboid shape with a rectangular floor measuring 11 m × 14.3 m. Water depth is 1.3 m. Water was pumped from the tank into barrels with a capacity of 3.9 hl. How many barrels were used, if the water level in the tank fallen 3 cm? Wri - Vinegar 2

How many percentage of getvinegar solution, if we mix to 14.5 liters of 7.8% and 2.5 liters of 5.8% vinegar? - Circle arc

Circle segment has a circumference of 13.26 mm and 252.03 mm^{2}area. Calculate the radius of the circle and size of central angle. - Cylinders

Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much? - Flags

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

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - Time

Write time in minutes rounded to one decimal place: 1 h 42 m 22 s. - Numbers

Determine the number of all positive integers less than 2937474 if each is divisible by 11, 23, 17. What is its sum? - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ? - Density - simple example

Material of density of 1278 kg/m^{3}occupies a container volume of 80 cm^{3}. What is its mass?

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