Equation + planimetrics - practice problems - page 27 of 28
Number of problems found: 543
- Proof PT
Can you easily prove Pythagoras' theorem using Euclidean theorems? If so, do it. - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c - Euclid3
Calculate the height and sides of the right triangle if one leg is a = 81 cm and the section of hypotenuse adjacent to the second leg cb = 39 cm. - Euclid1
The right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
- Circles
The areas of the two circles are in the ratio 2:20. The larger circle has a diameter 20. Calculate the radius of the smaller circle. - Gear
Two gears fit into each other and have a transfer of 2:3. Centers of gears are spaced 82 cm. What are the radii of the gears? - Resistors
Two parallel resistors connected in series give the resulting resistance $R1Ω and $R2Ω. Determine the resistance of these resistors. - R triangle
Calculate the right triangle area whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Coin
How many 20-cent coins must be put in a row that the next 20-cent coins after them (above) rolled on its axis?
- Triangle P2
Can a triangle have two right angles? - Proof I
When added to the product of two consecutive integers larger one, we get the square larger one. Is this true or not? - Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle. - Heron backlaw
Calculate the missing side in a triangle with sides 25 and 13 and area 152. - Right triangle
The legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
- Father and son
Father and son are 74 years old together. Son is 30 years younger than father. How old is the son? - Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle center. - RT - hypotenuse and altitude
The right triangle BTG has hypotenuse g=117 m, and the altitude to g is 54 m. How long are hypotenuse segments? - Rectangle
The area of a rectangle is 546. Its length is 25 larger than the width. What are the dimensions of the rectangle? - Chickens and rabbits
In the yard were chickens and rabbits. Together they had 23 heads and 76 legs. How many chickens and how many rabbits were in the yard?
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