# Examples for 8th grade - page 94

1. Rhombus construction Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
2. Competitors In the first round of slalom fell 15% of all competitors and in the second round another 10 racers. Together, 40% of all competitors fell. What was the total number of competitors?
3. Five pumps The water tank is filled with two pumps in 48 minutes. How long would it take to fill it with 5 same pumps?
4. 6 terms Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
5. Fence and scale The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
6. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
7. Soaps Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
8. Lighthouse The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
9. Trapezium bases Find the trapezium height if a = 8 cm and c = 4 cm if its content 21 square centimeters.
10. Diamond diagonals Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
11. Trapezoid ABCD ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD.
12. Paul earned Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t
13. Square area Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area .
14. Summands Find two summands of the number 42, so that its product is minimized.
15. Road The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
16. Percentages 5 \$5.25 is 7 1/2% of what number?
17. Digit sum The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
18. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?
19. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
20. Windbreak A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?

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