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

1. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
2. 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?
3. Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
4. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
5. 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°.
6. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
7. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
8. Is right?
Is triangle with sides 51, 56 and 77 right triangle?
9. Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 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?
10. 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 ?
11. 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
12. 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.
13. Rectangle SS
Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
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?
15. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
16. 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.
17. Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
18. Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
19. 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?
20. 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?

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Pythagorean theorem is the base for the right triangle calculator.