Garden

The garden has the shape of a rectangle measuring 19m20cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent pillars to be the same on all sides. What is the distance between the pillars?

Result

x =  240 cm

Solution:

a=19 100+20=1920 cm b=21 100+60=2160 cm 1920=2735 2160=24335 GCD(1920,2160)=2435=240  s=GCD(a,b)=GCD(1920,2160)=240 200<x<300 x=s=240 cma=19 \cdot \ 100+20=1920 \ \text{cm} \ \\ b=21 \cdot \ 100 + 60=2160 \ \text{cm} \ \\ 1920=2^7 \cdot 3 \cdot 5 \ \\ 2160=2^4 \cdot 3^3 \cdot 5 \ \\ \text{GCD}(1920, 2160)=2^4 \cdot 3 \cdot 5=240 \ \\ \ \\ s=GCD(a,b)=GCD(1920,2160)=240 \ \\ 200<x<300 \ \\ x=s=240 \ \text{cm}



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Do you want to calculate least common multiple two or more numbers?
Do you want to calculate greatest common divisor two or more numbers?
Do you want to convert length units?

Next similar math problems:

  1. Spartakiada
    spartakiada_1 Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100?
  2. Trees in alley
    tree_6 There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them?
  3. Bicycle wheels
    kolo_1 Driving wheel of a bicycle has 54 teeth. The driven wheel has 22 teeth. After how many revolutions will meet the same teeth?
  4. Biketrial
    cyklo Kamil was biketrial. Before hill he set the forward gear with 42 teeth and the back with 35 teeth. After how many exercises (rotation) of the front wheel both wheels reach the same position?
  5. Apples 2
    jableka How many minimum apples are in the cart, if possible is completely divided into packages of 6, 14 and 21 apples?
  6. Length of a string
    meter What is the smallest length of a string that we can cut into 18 equal parts and even 27 equal parts (in decimeters)?
  7. LCM
    numbers_11 Common multiple of three numbers is 3276. One number is in this number 63 times, second 7 times, third 9 times. What are the numbers?
  8. Dance ensemble
    dancers_1 The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six and nine. How many dancers have an ensemble?
  9. LCM of two number
    numbers2_19 Find the smallest multiple of 63 and 147
  10. Lcm simple
    lcm_gears Find least common multiple of this two numbers: 140 175.
  11. Children's home
    jablka The children's home received a gift to Nicholas of 54 oranges, 81 chocolate figurines, and 135 apples. Every child received the same gift and nothing was left. a) How many packages could be prepared? b) what did the children find in the package?
  12. Balls groups
    gulky_5 Karel pulled the balls out of his pocket and divide it into the groups. He could divide them in four, six or seven, and no ball ever left. How little could be a ball?
  13. School books
    sesity At the beginning of the school year, the teacher distributed 480 workbooks and 220 textbooks. How many pupils could have the most in the classroom?
  14. Dance group
    dancers The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
  15. MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  16. LCD 2
    zlomky_6 The least common denominator of 2/5, 1/2, and 3/4
  17. Gears
    ozub_kola The gearing fits wheel with 20 teeth to the wheel with 36 teeth. Before starting the machine is stained tooth smaller wheels in the designated space between the teeth of the larger wheels. How many times after starting the machine wheels turning that stain