Ratio + Pythagorean theorem - practice problems - page 2 of 4
Number of problems found: 77
- Railway embankment
The railway embankment section is an isosceles trapezoid, and the bases' sizes are in the ratio of 5:3. The arms have a length of 5 m, and the embankment height is 4.8 m. Calculates the size of the embankment section area. - 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 square's side and the circle's arc. What is the ratio of the areas of the large and small squares? - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles.
- Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Cross-section 23491
The cross-section of the railway embankment is an isosceles trapezoid, the bases of which are in a ratio of 5:3. The arms have a 5 m embankment height v = 4.8 m. Calculate the section area S. - 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. - Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side.
- The aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs lengths 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. - Ratio of sides
Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in a ratio of 2 to 7.
- Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - 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. - Rectangular field
A rectangular field has a diagonal length of 169m. If the length and width are in the ratio of 12:5. Find the dimensions of the field, the perimeter of the field, and the area of the field. - Circumference 7615
The sides of the rectangle are in a ratio of 3:5. Its circumference is 48 cm. Calculate the length of its diagonal. - Rectangular garden
The sides of the rectangular garden are in a ratio of 1:2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
Do you have homework that you need help solving? Ask a question, and we will try to solve it.