# Pythagorean theorem + quadratic equation - math problems

#### Number of problems found: 81 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 cm3. 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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