Square into three rectangles

Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.

Result

a =  12
b =  3
c =  9
d =  6
o1 =  30
o2 =  30
o3 =  30
o4 =  32

Solution:


a=12
o1 = 2(a+b)
o2 = 2(c+d)
o3 = 2(c+d)
o1=o2
b+c=a
2d = 12
o4 = 2(a+a/3)

a = 12
2a+2b-o1 = 0
2c+2d-o2 = 0
2c+2d-o3 = 0
o1-o2 = 0
a-b-c = 0
2d = 12
8a-3o4 = 0

a = 12
b = 3
c = 9
d = 6
o1 = 30
o2 = 30
o3 = 30
o4 = 32

Calculated by our linear equations calculator.








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

Showing 1 comment:
#1
Dr Math
so the solution is

1. 12*3 ...  a = 12 * b = 3
2. 9*6 ... c = 9 * d = 6
3. 9*6 ... c = 9 * d = 6

o1 is the circumference of the first, o2 the second, o3 the third rectangle
o4 is a circumference if the square is divided into same   12 * 4 rectangles

avatar









To solve this example are needed these knowledge from mathematics:

Do you have a system of equations and looking for calculator system of linear equations?

Next similar examples:

  1. Gardens
    garden_3 The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
  2. Garden plot
    plot Calculate how many meters of fence need to fence the square garden with length and width of 22 meters.
  3. Area of square
    big-square Calculate the content area of the square whose perimeter is 24 dm.
  4. Perimeter of square
    stvorec_1 The square has a circumference 17cm. What is its area?
  5. Fence
    zahrada-rd Square garden has an area of 537 m2. How many meters netting is necessary to fence the garden?
  6. Unknown number 24
    ctverce I think the number: a - is the same as the square area that has the 12th circumfence. What is this number? b - its half is 7 times bigger than its quarter. Is this the number?
  7. Foot in bus
    havo It was 102 people on the bus. 28 girls had two dogs. A 11 girls had one dog. At the next stop seceded 5 dogs (even with their owners). They got two boys together with three dogs. The bus drove one driver. How many foot were in bus?
  8. Cages
    guineapig Honza had three cages (black, silver, gold) and three animals (guinea pig, rat and puppy). There was one animal in each cage. The golden cage stood to the left of the black cage. The silver cage stood on the right of the guinea pig cage. The rat was in the
  9. Three days
    skolske-zosity_1 During the three days sold in stationery 1490 workbooks. The first day sold about workbooks more than third day. The second day 190 workbooks sold less than third day. How many workbooks sold during each day?
  10. Triangle ABC
    triangles_6 In a triangle ABC side b measure 10 cm less than the side a and side b is half of the side c. Calculate the length of sides if the circumference of the triangle is 42 cm.
  11. Clock hands
    clocks2_16 The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
  12. Turtles Žofka and Julka
    korytnacky Gray wolf kept in his tent turtles Žofka and Julka, which together have 200 years. After 50 years will Julka 2 times older than Žofka. How old are the turtles?
  13. Subjects
    math_series_1 Student makes a mathematical task for five minutes and the task from biology in twelve minutes. Another day he have homework in math and biology which consists of eleven tasks together. To do the job took hour and a half. How many tasks maked in each subje
  14. Father and son
    father_son Father and son are together 80 years. Son is 28 years younger than father. How old is the son?
  15. The store
    carot The store received the same number of cans of peas and corn. The first day sold 10 cans of peas and 166 cans ofcorn so that left 5 times more peas than corn cans. How many cans of each kind were in the store?
  16. Velocipede
    velociped The front wheel of velocipede from year 1880 had a diameter 1.8 m. If the front wheel turned again one then rear wheel 6 times. What was the diameter of the rear wheel?
  17. Bob and Bobek
    carot_1 Bobek has 2 cabbages and 5 carrots, Bob has 2 cabbages and 9 carrots. When Bobek stepped on the scale weight 5800 g and when Bob weight 8960 g. Actual Bob weight is 8 kg and Bobek 5 kg. How much weighs one carrot?