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

#### Number of problems found: 53

• Two parallel chords
In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm.
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?
• A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain?
• Trip with compass
During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
• Triangular pyramid
A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
• Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
• Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
• Two diagonals
The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
• Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
• Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.
• 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.
• Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
• Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
• 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.
• Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
• Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
• Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
• Hypotenuse
Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
• AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
• Square
Calculate the side of a square with a diagonal measurement 10 cm.

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