# Pythagorean theorem + square (second power, quadratic) - examples

- Ladder

Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder? - Garden

Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden? - Rectangle

The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle. - Circle chord

What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m? - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 16 km/h. Determine the distance between them after 35 minutes cycling. - Square

Points A[-10,-1] and B[2,-1] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Short cut

Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Rectangle SS

Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle. - Ladder

Ladder 8 m long is leaning against the wall. It foot is 1 m away from the wall. In which height ladder touch the wall? - Without Euclid laws

Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws. - Square 2

Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Circle

Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ? - Tank

In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank? - Chord

In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Arc

Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.

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Pythagorean theorem is the base for the right triangle calculator.