# Pythagorean theorem - examples - page 23

- ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX? - Ratio of edges

The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Body diagonal

Calculate the volume and surface of the cube if the body diagonal measures 10 dm. - Quadrangular pyramid

Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area. - Is right triangle or not

If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. - Ellipse

Ellipse is expressed by equation 9x^{2}+ 25y^{2}- 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse. - Is right-angled

Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle? - Cube diagonals

The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Nonagon

Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm - Body diagonal

Calculate the length of the body diagonal of the 6cm cube. - The pond

We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond? - Cone 15

The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height? - Find radius

Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.

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Pythagorean theorem is the base for the right triangle calculator.