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. TV transmitter
    praded The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
  2. Pool
    pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
  3. Cuboid
    cuboid Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm3. Calculate the length of the other edges.
  4. Coffee
    coffe In stock are three kinds of branded coffee prices: I. kind......248 Kč/kg II. kind......134 Kč/kg III. kind.....270 Kč/kg Mixing these three species in the ratio 10:7:7 create a mixture. What will be the price of 1100 grams of this mixture?
  5. Three brothers
    family_13 The three brothers have a total of 42 years. Jan is five years younger than Peter and Peter is 2 years younger than Michael. How many years has each of them?
  6. Barrel with water
    sudy_5 The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
  7. Store
    pave One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
  8. Motion
    cyclist_1 If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure. How far is the train station?
  9. Forestry workers
    forestry_workers In the forest is employed 43 laborers planting trees in nurseries. For 6 hour work day would end job in 35 days. After 11 days, 8 laborers go forth? How many days is needed to complete planting trees in nurseries by others, if they will work 10 hours a da
  10. Linear system
    linear_eq_2 Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
  11. Two diggers
    digging Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
  12. Tickets 4
    cinema2_13 Stacey is selling tickets to the school play. The tickets are $7 for adults and $5 for children. She sells twice as many adult tickets as children's tickets and brings in a total of $342. How many of each kind of ticket did she sell?
  13. Supplementary angles
    susedne_huly One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
  14. Two resistors
    two_resistors Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
  15. Equations - simple
    linearna_1 Solve system of linear equations: x-2y=6 3x+2y=4
  16. Integer
    abs1 Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
  17. Excavation
    vykop_ryha Mr. Billy calculated that excavation for a water connection dig for 12 days. His friend would take 10 days. Billy worked 3 days alone. Then his friend came to help and started on the other end. On what day since the beginning of excavation they met?