Ratio + similarity of triangles - practice problems - page 2 of 4
Number of problems found: 63
- Circumference 42471
The lengths of the sides of the triangle ABC are in the ratio 4:2:5. Calculate the size of the longest side of a similar KLM triangle, whose circumference is 66 cm. - A cliff
A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high. It meets the ground at a point 8 ft from the base of the pole. The point is 93 ft from the base of the cliff. How high is the cliff? - Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long simultaneously. - 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.
- Vertical 29801
The shadow of the building is 16 m long, and the shadow of the vertical meter rod is 0.8 m long at the same time. What is the height of the building? - The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m? - Chimney and tree
Calculate the height of the factory chimney, which casts a shadow of 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - Similar triangles
The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - Triangle 28611
The land has a triangle shape with sides of 300m, 200m, and 245m. Draw it on a scale of 1:5 000.
- 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? - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - Similarity coefficient
In the triangle TMA, the length of the sides is t = 5cm, m = 3.5cm, and a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, and 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Meneal's 26771
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - Similarity 26441
How long a shadow casts a building 15 m high if the shadow of a meter rod is 90 cm? Sketch - similarity.
- Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Approximately 25381
The observer sees the tops of two trees at the same angle a. It is 9 m from one tree and 21 m from the other. The trees stand on a level. How tall is the second tree if the height of the first is 6 m? Remember that the eyes of a standing person are approx - 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. - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
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