# Pythagorean theorem + ratio - math problems

#### Number of problems found: 52

• Centre of the hypotenuse For the interior angles of the triangle ABC, alpha beta and gamma are in a ratio of 1: 2: 3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB.
• The diamond The diamond has an area S = 120 cm2, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond.
• 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
• Ratio of triangles areas In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the area
• Railway embankment The railway embankment section is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m, and the height of the embankment is 4.8 m. Calculates the size of the embankment section area.
• 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.
• 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
• 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 ratio 5:3. Find its side lengths.
• 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 ratio 2 to 7.
• 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 of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.
• Rectangular garden The sides of the rectangular garden are in ratio 1: 2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden.
• The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
• The diamond The diamond has sides of 35 cm and the diagonals are in a ratio of 1: 2. Calculate the lengths of the diagonals.
• The sides The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals
• Two diagonals The diagonals of the diamond EFGH have lengths in the ratio 1: 2. What is the circumference of a rhombus if the longer of the diagonals is 8 cm long?
• Isosceles trapezoid Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
• Rectangle 35 Find the rectangle area when the diagonal is equal to 30 cms and the width is double the length.
• Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.

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