# Natural numbers + quadratic equation - problems

1. Rectangle diagonals
It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
2. Euler problem
Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
3. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
4. Sequence
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
5. Four integers
Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
6. MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
7. 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?
8. Find two
Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.

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