Square gardens

The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.

Correct result:

a =  60 m
n =  15

Solution:

$$\begin{gathered} x=180\text{ m } \\ y=300\text{ m } \\ 180=2^2\cdot 3^2\cdot 5 \\ 300=2^2\cdot 3\cdot 5^2 \\ \text{GCD}(180,300)=2^2\cdot 3\cdot 5=60 \\ a=GCD(x,y)=GCD(180,300)=60\text{ m} \end{gathered}$$

$n=x\mathrm{/}a\cdot (y\mathrm{/}a)=180\mathrm{/}60\cdot (300\mathrm{/}60)=15$

Try another example

Showing 0 comments:

Next similar math problems:

• Gardens colony
  Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
• Cutting paper
  Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.
• Plumber
  The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
• Tiles
  Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
• Wide field
  The field is 203 meters wide 319 meter long, what is the greater length of the rope by which length and width can be measured and find the exact number of time.
• Glass panel
  A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Largest squares
  How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?
• Bundle of candies
  In the store has 168 chocolates, caramel candies 224 and 196 hard candies. How many packages we can do and how many of candies will be in each package?
• Sports students
  There are 120 athletes, 48 volleyball players, and 72 handball players at the school with extended sports training. Is it possible to divide sports students into groups so that the number in each group is the same and expressed by the largest possible num
• Square tiles
  The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor.
• Around the flowerbed
  Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses found in every corner of the flowerbed and consumed them as little as possible. a) At what distance are planted roses? b) How many ros
• Tissues
  The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than
• Paper squares
  The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.
• Pexeso
  Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?
• Tiles
  The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.
• School books
  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?
• Quotient
  Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33