# 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. - Right

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: ? - Catheti

The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs. - Cuboid

Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm^{3}. Calculate the length of the other edges. - Rhombus

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). - Triangle

Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17. - Circle

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. - Semicircle

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.

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