Ratio + square (second power, quadratic) - practice problems
Number of problems found: 68
- Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - The ratio 7
The ratio of the sides of two squares 4:5 if the sum of their areas is 180 cm² Find the sides of the two squares. - Square function
If z varies jointly as x and the square of y, and z = 20 when x = 4 and y = 2, find z when x = 2 and y = 4. - Markus painter
Markus used ¾ liter of paint to cover 10 ½ square meters of wall. How many liters of paint is needed to cover 12 ¼ square meters of wall? - Ratio in trapezium
The height v and the base a, c in the trapezoid ABCD are in the ratio 1: 6: 3, its content S = 324 square cm. Peak angle B = 35 degrees. Determine the perimeter of the trapezoid - Cuboid - ratio
Find the volume of a block whose dimensions are in the ratio 2: 3: 4 and the surface is 117 dm². - Cuboid edges
The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m². - Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares? - The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm². What is its length? - Half of halves
Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part? - Squares ratio
The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte - Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc - Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square. - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths. - Two rectangles 2
A square of area 36 cm² is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B. - Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm². - Three gardens
Is it possible to divide a plot of land with an area of 920 m² into three gardens in a ratio of 4: 2: 3 so that their areas are only whole multiples of square meters? - The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid's area is 245. Find the height and the perimeter of the trapezoid. - In the In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km². What area is wooded?
- Two gears
A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
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