# Square (second power, quadratic) + Pythagorean theorem - math problems

1. 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.
2. Garden Area of a 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 50 dm, if the distance from the center circle is 21 dm?
4. Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
5. Triangle SAS Calculate the 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[-9,7] and B[-4,-5] 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. 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.
13. 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. Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall?
15. Rectangle SS Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
16. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
17. 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. The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 36 km/h and ambulance 47 km/h. Calculate such a relative speed of the ambulance moves to the car.
19. Square 2 Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
20. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?

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Pythagorean theorem is the base for the right triangle calculator.