System of equations + area - math problems

Number of problems found: 63

  • 144 steps
    To get around the garden we have to take 144 steps. 8 steps less in width than in length. One step is 5 decimetres long. What are the dimensions of the garden? What is its perimeter and its area?
  • Louis
    Louis wants to carpet the rectangular floor of his basement. The basement has an area of 5,120 square feet. The width of the basement is 4/5 its length. What is the length of Louis's basement?
  • Truncated pyramid
    The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base.
  • The block
    The block, the edges formed by three consecutive GP members, has a surface area of 112 cm2. The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block.
  • Harry
    Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Fi
  • Outside point
    The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4?
  • The cylinder
    In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm2 and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
  • Rotary cylinder
    In the rotary cylinder it is given: surface S = 96 cm2 and volume V = 192 cm cubic. Calculate its radius and height.
  • Arm and base
    The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
  • 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.
  • Area and perimeter of rectangle
    The content area of the rectangle is 3000 cm2, one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
  • Dimensions of the trapezoid
    One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2
  • Sow barley
    Farmers wanted to sow barley within 13 days. Due to the excellent weather, they exceeded the daily plan of sowing by 2 ha and therefore finished sow grain in 12 days. How many hectares of land did they sow with barley?
  • In the
    In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
  • Coordinates
    Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
  • The circumference
    The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  • Side lengths
    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.
  • An equilateral
    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?
  • Block or cuboid
    The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
  • Two gardens
    The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?

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