Ratio + planimetrics - practice problems - page 2 of 19
Number of problems found: 368
- Snowman's 82155
Under the column, the children built a 1.65m tall snowman. The snowman's shadow is 135 cm long. The shadow of the column has a length of 4.05 m. How tall is the pole? - Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence. - Dimensions 81780
The garden is 24m long and 15m wide. Determine the ratio of the dimensions of this rectangle. - Dimensions 81779
The picture for the textbook was reduced to a ratio of 2:5. What are the dimensions of the reduced image if the original dimensions were 20 cm and 15 cm?
- Rectangle's 81596
The rectangle has a perimeter of 30 cm. The ratio of its sides a: b=2:3. Calculate the sides' lengths and the rectangle's area. - 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 - Square-shaped 81445
The area of the square-shaped room on the drawing with a scale of 1:150 is 6 cm square. Determine the actual area of the room in square meters. - Perimeters 81399
Two squares are given. The first has a side length of 5 cm, the second 10 cm. Write the ratio of: for a- of their sides for b- their perimeters for c- their areas - Square 81238
A forest with a square plan has an area of 4 square km. What side will the square have on a 1:50,000 scale map?
- Rectangular 81233
A rectangular strip of paper measuring 4 cm x 13 cm is folded as shown. The two resulting rectangles have areas P and Q, where P = 2Q. Calculate the value of x. Note divide the side of 13 cm by x and 13-x. - Complementary 81152
In a certain polygon, the ratio of the sum of the sizes of its internal angles and the sum of the sizes of the complementary angles is 2:5. How many vertices does this polygon have? - Right-angled 81150
In the right-angled triangle ABC (the right angle at vertex C), the angle ratio is α : β = 5 : 3. Calculate the sizes of these angles and convert them to degrees and minutes (e.g., 45°20') - Relatively 81129
The sides of the rectangle are relatively 5:4, and the perimeter of the rectangle is 308 dm. Find the area of the rectangle. - Right-angled 81126
In a right-angled triangle, the hypotenuse has a length of 24 cm. The heel of the height on the hypotenuse divides it into two parts in a ratio of 2:4. What size in cm is the height at the hypotenuse? Calculate the perimeter of this right triangle in cent
- Right-angled 81019
In the right-angled triangle ABC (AB is the hypotenuse), a : b = 24 : 7, and the height to the side c = 12.6 cm applies. Calculate the lengths of the sides of triangle ABC. - Smaller 81015
Divide the content of the garden in the shape of a square S=153m² in a ratio of 2:7. What part of the garden does the smaller part occupy? - 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. - Perimeter 80853
The lengths of the sides of the triangle are in the ratio 7:6:4. The shortest side is 36 cm. What is the perimeter in cm of this triangle? - Equilateral 80851
Kornelia cut off the colored part from the equilateral triangle. The shortest side of the colored triangle is 1/3 the length of the side of the original triangle. Calculate what part of the triangle she cut off.
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