# Pythagorean theorem + expression of a variable from formula - problems

- Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2.}Calculate content of square over the triangle's hypotenuse. - 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? - 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? - Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F. - Right Δ

Right triangle has length of one leg 68 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 39 cm, c = |CD| = 8 cm and legs b = d = |BC| = |AD| = 24 cm. - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel. - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 128 mm. - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm. - Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm^{2.} - Cone and the ratio

Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface. - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Rectangle diagonals

It is given rectangle with area 24 cm^{2}a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Chord

In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2.}Calculate the deviation of the side of this cone from the plane of the base. - Nice prism

Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Rectangle

The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle. - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag

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Pythagorean theorem is the base for the right triangle calculator.