# Similarity of triangles - practice problems - page 2 of 8

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 152

- Figure 2

Figure A maps to figure B with a scale factor of 0.75. The length of the line AB segment in figure A is 10. What is its length on the image in figure B? - Karim

Karim uses a photocopier to enlarge the triangle PQR diagram by 150%. a) Write the ratio of the length of P' Q' to the length of PQ. b) Is the ratio of the length P 'R' to the length PR equal to the ratio of the length P 'Q' to the length PQ? c) Use your - 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, 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?

- 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? What is the area of the triangle? - Length 26

The 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: - Isosceles 67744

Two isosceles triangles have the same angle at the vertex opposite the base. The first one has a base of 12 cm and a leg of 9 cm. The other has a 16 cm long base. Calculate the perimeter of the second triangle. - 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 line BC is perpendicular to line AB, and EA is perpendicular to line AB. Point P is the heel of the vertical starting from point D on line AB. | AP | = | PB |, | BC | = | EA | = 6dm, | PD | = 8.4dm - 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, and 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, two 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.

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