Rectangle + right triangle - math problems

1. Area of a rectangle Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
2. Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
3. Rectangle In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
4. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
5. 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
6. Rectangle Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
7. Rectangle In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
8. Circular pool The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
9. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
10. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
11. Triangular prism The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
12. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
13. Carpet The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
14. Median In the right triangle are sides a=41 dm b=42 dm. Calculate the length of the medians tc to the hypotenuse.
15. TV diagonal Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9? 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
17. Again saw From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
18. Acreage What acreage has a rectangular plot whose diagonal is 34 meters long and one side has a length of 16 meters. ?
19. Diagonal 20 Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
20. Dig water well Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?

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