Fractions + similarity of triangles - practice problems
Number of problems found: 16
- A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts. - Shadow 73354
How long is the shadow of a tree 7.6 m high, and the shadow of a 190 cm high road sign is 3.3 m long? - Determine 70834
At the same time, a vertical 2-meter pole casts a shadow of 0.85 meters. At the same time, a chimney of unknown height casts a 45m long shadow. Determine the height of the chimney. - Shadows
At the park, a young woman who is 1.72 meters tall casts a 3.5 meters shadow at a certain hour. What is the height of a tree in the park that, at the same time, casts a 12.3 meters shadow? - The shadow
The shadow of a 1 m high pole thrown on a horizontal plane is 0.8 m long. At the same time, the shadow of a tree thrown on a horizontal plane is 6.4 m. Determine the height of the tree. - Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if a column 2.5 m high has a shadow of 1.5 m at the same time. - Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D'E'F' is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D'E'F' if the similarity coefficient is one-seventh. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Rectangular triangles
The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the areas of these triangles? A smaller rectangular triangle has legs 6 and 8 c - MO Z9–I–2 - 2017
VO is a longer base in the VODY trapezoid, and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm². Find the area of the entire trapezoid. - Cone
The circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Find all
Find all right-angled triangles whose side lengths form an arithmetic sequence. - Triangle 69144
The line p passes through the center of gravity T of the triangle and is parallel to the line BC. What is the ratio of the area of the divided smaller part of the triangle by the line p? What is the area of the triangle? - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - Calculate 64444
The length of the linden shadow is 429 cm. The length of the shadow meter is 78cm. Calculate the height of the linden. - Triangle-shaped 30011
Determine the map's scale if the 1.6 km, 2.4 km, and 2.7 km triangle-shaped forests are drawn on the map as a triangle with sides of 32 mm, 48 mm, and 54 mm.
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