Pythagorean theorem + quadratic equation - math problems

Number of problems found: 81

  • Find radius
    numbers_49 Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
  • Rectangle SS
    rectangle Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
  • Equation of circle 2
    circle_axes Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
  • Distance problem
    linear_eq_3 A=(x, x) B=(1,4) Distance AB=√5, find x;
  • Right triangle
    righttriangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  • Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  • Distance problem 2
    geodetka_1 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
  • Find parameters
    circle_axes_1 Find parameters of the circle in the plane - coordinates of center and radius: ?
  • Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  • Cuboid
    cuboid Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  • Rhombus
    rhombus2_3 The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
  • Surface area of the top
    cylinder_4 A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
  • Sphere equation
    sphere2 Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
  • Triangle
    Triangle_trig Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
  • Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  • Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  • Semicircle
    semicircle_2 To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
  • Triangle ABC
    squares4 Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled?
  • Integer sides
    rt_triangle_1 A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
  • RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.

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