Pythagorean theorem + quadratic equation - math problems
Number of problems found: 81
- Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
- Rectangle SS
Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
- Equation of circle 2
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
A=(x, x) B=(1,4) Distance AB=√5, find x;
- Right triangle
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.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
- Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
- Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
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
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
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).
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
- Secret treasure
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.
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
- Triangle ABC
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
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
- RT and circles
Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
Looking for help with calculating roots of a quadratic equation? Pythagorean theorem is the base for the right triangle calculator.