System of equations + expression of a variable from the formula - math problems

  1. The circumference
    rectangle The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  2. Side lengths
    triangles_1 In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  3. Wire fence
    plot_zed The wire fence around the garden is 160 m long. One side of the garden is three times longer than the other. How many meters do the individual sides of the garden measure?
  4. In a
    triangles_1 In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
  5. An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
  6. Block or cuboid
    cuboid The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  7. Conical bottle
    cone-upside When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
  8. Two patches
    krizik Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of t
  9. Two-digit number
    numbers_1 Digit sum of thinking two-digit natural number is 11. When it exchanging a sequence of digits, given a number which is 27 less than the thinking number. Find out which number I think.
  10. Together m+w
    workers Women 30%. Men are 360 more. How many are together?
  11. Rectangle field
    land The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
  12. Flowerbed
    circles We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
  13. Sides of right angled triangle
    triangle_rt1 One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
  14. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
  15. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  16. GP - three members
    progression_ao The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
  17. Two cubes
    cubes2 The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
  18. Hyperbola equation
    hyperbola_4 Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
  19. Isosceles triangle
    iso_tr_1 In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
  20. Rectangular plot
    rectangular plot The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot.

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