# Pythagorean theorem - problems - page 18

1. Diagonal of the rectangle
Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
2. 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?
3. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
4. Square
Calculate the side of a square with a diagonal measurement 10 cm.
5. Trio 2
Decide whether trio of numbers is the side of a right triangle: 26,24,10.
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
7. Flowerbed
Family cultivated tulips on a square flower bed of 6 meters. Later they added the square terrace with a side of 7 meters to their house. One vertex of the terrace lay exactly in the middle of a tulip bed, and one side of the terrace divided the side of the
8. Four ropes
TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
9. Cableway
Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
10. Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
11. Isosceles trapezoid
Calculate the circumference and the contents of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm and the size of the arms is 5 cm.
12. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
13. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
14. Church roof 2
The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
15. Chord circle
The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
16. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
17. Hypotenuse
Calculate the length of the hypotenuse of a right triangle with a cathetuses 71 cm and 49 cm long.
18. Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
19. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.