Similarity of triangles - practice problems
Number of problems found: 119
- 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?
- Shadows
At the park, at certain hour, there is a young woman who is 1.72 meters tall that casts a 3.5 meters shadow. What is the height of a tree of the park that, at the same time, casts a 12.3 meters shadow?
- 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.
- 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 and the area of the triangle?
- Length 26
Length of the median of the trapezoid is 10 inches. The median divides the trapezoid into two areas whose ratio is 3:5. The length of the shorter base is:
- 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.
- Circumference 64104
The ABC triangle has a circumference of 11 cm. Triangle A'B'C ', similar to triangle ABC, has side lengths of 6 cm, 120 mm, and 1.5 dm larger than triangle ABC. Calculate the area of the triangle A'B'C '.
- Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?
- Pentagon
The signboard has the shape of a pentagon ABCDE, in which the line BC is perpendicular to the line AB and EA is perpendicular to the line AB. Point P is the heel of the vertical starting from point D on line line AB. | AP | = | PB |, | BC | = | EA | = 6dm
- Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle
- Calculate
Calculate the height of a tree that casts a shadow 22 m long, if you know that at the same time a pillar 2 m high casts a shadow 3 meters long.
- Similarity of triangles
If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place.
- Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal areas perpendicular to the axis of symmetry (into a trapezoid and a triangle)?
- Two similar
Two similar triangles, one has a circumference of 100 cm, the second has sides successively 8 cm, 14 cm, 18 cm longer than the first. Find the lengths of its sides.
- The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
- Two cables
On a flat plain, 2 columns are erected vertically upwards. One is 7 m high and the other 4 m. Cables are stretched between the top of one column and the foot of the other column. At what height will the cables cross? Assume that the cables do not sag.
- Tower's view
From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church.
- MO Z7–I–6 2021
In the triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE and CBD are 30°, 60°, 20° and 30°, respectively. Find the size of the AED angle.
- 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 and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the cliff, how high is the cliff?
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