# Inequalities - examples

1. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
2. 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
3. R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
4. Rates
When gas consumption, the consumer may choose one of two rates: rate A - which pays 0.4 € per 1 m3 of gas a flat monthly fee of 3.9 € (regardless of consumption) rate B - which pays 0.359 € per 1 m3 of gas a flat monthly fee of 12.5 € From what monthl
5. Report card
Ivor hit 5× grade 5 at the beginning of the school year. How many times must now catch grade 1 to get grade 2 on report card?
6. Built-up area
John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
7. Car factory
Carmaker now produce 4 cars a day more than last year, so the production of 388128 cars will save just one full working day. How many working days needed to manufacture 388128 cars last year?
8. 3-bracket
May be the largest angle in the triangle less than 20°?
9. Intersections
How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
10. Party
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
11. Line
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
12. 3-bracket 2
May be the smallest angle in the triangle greater than 40°?
13. 3-bracket 3
Two angles in a triangle are 90° and 60°. Has triangle at least two equal sides?
14. Triangle
For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
15. Circle chord
Determine the radius of the circle in which the chord 6 cm away from the center of the circle is 12 cm longer than the radius of the circle.
16. Trees
Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
17. Lion or virgin
We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
18. Reciprocal
It is true (prove it) that if a> b> 0: ?
19. QuizQ
An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
20. Mr. John
Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150.

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