# Similarity of triangles - practice problems

Direction: Solve each problem carefully and show your solution in each item.#### Number of problems found: 147

- 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. - Two similar 2

Two similar polygons have corresponding sides 15 inches and 6 inches. If the area of the first is 2700 square inches, what is the area of the second? - Scale model

In a model train set, 1.38 inches represents one foot in real life. The height of One World Trade Center in New York City is 1776 feet. How tall would a scale model of the building be? Should you calculate 1776 x 1.38 or 1776 ÷ 1.38? - Observation 82811

From the 40 m high observation deck, you can see the top of the poplar at a depth angle of 50*10' and the bottom of the poplar at a depth angle of 58*. Calculate the height of the poplar. - Mast angles and height

Calculate the height of the mast, whose foot can be seen at a depth angle of 11° and the top at a height angle of 28°. The mast is observed from a position 10 m above the level of the base of the mast. - Determine 82470

The school building casts a shadow 16 m long on the plane of the yard, and at the same time, a vertical meter pole casts a shadow 132 cm long. Determine the height of the building. - Triangle 81484

Choose a triangle that is similar to the given triangle. - ∆ TFC= t= 8 cm, f= 9 cm, c= 7 cm. : ∆ PKU= p= 45 cm, k= 35 cm, u= 40 cm. ∆ UPK= u= 40 cm, p= 45 cm, k= 35 cm. ∆ PUK= p= 45 cm, u= 40 cm, k= 35 cm. ∆ KPU= k= 35 cm, p= 45 cm, u= 40 cm. ∆ KUP= k= 35 - Triangles 81480

Decide whether the triangles are similar. Choose between Yes/No. ∆ YUO: y= 9m, u= 17 m, o= 12 m, ∆ ZXV= z= 207 dm, x= 341 dm, v= 394 dm - Centimeters 80859

Triangle ABC and triangle ADE are similar. Calculate in square centimeters the area of triangle ABC if the length of side DE is 12 cm, the length of side BC is 16 cm, and the area of triangle ADE is 27 cm². - Determine 80754

The perimeter of triangle MAK is 216 mm, side a = 81 mm, and side k = 62 mm. Determine the side length of the triangle OSA if the triangle MAK is congruent to the triangle OSA. - Right-angled 80745

The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - Similarity 80742

Calculate the perimeter of triangle ABC if you know that it is similar to triangle EFG in which e=144 mm, f=164 mm, g=92 mm, and the similarity ratio is 4. Express the result in cm. - Calculate 80741

In the camp, the children made a mock-up of the campsite. In its center was a maple, which had a height of 28 cm on the model. Calculate the height of the maple in the campsite if, in the morning, it casts a shadow 14 m long and its model has a shadow 49 - Nicolette

Nicolette makes a small bead bracelet using five red, eight purple, and six green beads. A large necklace has the same ratio of beads as a small bracelet. If the large necklace requires 15 red beads, how many purple beads are needed to make a large bracel - Find all

Find all right-angled triangles whose side lengths form an arithmetic sequence. - 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.

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