there is a field (112m x 75m) that are split into 13 square plots. What are the dimensions [must be in whole meters].

there is a picture, but the boxes are not to scale so i don't know how to get started on this problem. if someone could help me this would be great.


Want to do it painless?

Take the figure. You need a ruler. Assign the side of the smallest square as 1. Then, go to the next smallest adjoining square, and call its side x. Then, start working sides of squares from these two mumbers, determining lengths of the sides until you have them all done. At that point, you know the side lengths really are, so you have some functions of x that are equal to 112 and 75. Solve for x.

There is an analytic method, it is for crazy ap kids to work on for weeks.

Forget the ruler. I was initially sidegtracked. You don't need it with the painless method I gave you.

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OKAY TIME TO GET SERIOUS

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4 pennies in two lines in each line 3 cents how is this problem solved?

they would be placed in a X that way there are 2 lines and each had 3 because they each share 1 penny

To solve this problem using the painless method mentioned, follow these steps:

1. Start with the smallest square and assign its side length as 1 meter.
2. Move to the next smallest square, which is adjoining the first square. Assign its side length as 'x' meters.
3. Continue this process, assigning side lengths to the adjoining squares until you have covered all 13 squares.
4. Now, you have created a set of equations representing the lengths of the sides of each square.
5. Use the information given in the question to set up the equations:

- We know that the length of the field is 112 meters and the width is 75 meters.
- The length of the field can be expressed as the sum of the side lengths of all the squares.
- The width of the field can be expressed as the sum of the side lengths of 9 squares plus half of the side length of the 10th square.

6. Set up the equations as follows:

- Equation 1: x + 2x + 3x + ... + 13x = 112 (sum of the side lengths of all squares equals 112 meters)
- Equation 2: x + 2x + 3x + ... + 9x + (1/2)(10x) = 75 (sum of the side lengths of 9 squares plus half of the side length of the 10th square equals 75 meters)

7. Simplify both equations by summing arithmetic series:

- Equation 1: 91x = 112
- Equation 2: 45x + 5x = 75

8. Solve the equations to find the value of 'x':

- Equation 1: x = 112/91
- Equation 2: x = 75/50

9. Since the dimensions must be in whole meters, round both values of 'x' to the nearest whole number:

- x ≈ 1.23
- x ≈ 1.5

10. Finally, use the value of 'x' to calculate the dimensions of the field and each square:

- Length of the field = 13x ≈ 13.23 ≈ 13 meters
- Width of the field = 9x + 0.5x ≈ 9.73 ≈ 10 meters
- Dimensions of each square = x ≈ 1.23 ≈ 1 meter (rounded to the nearest whole number)

Therefore, the dimensions of the field are approximately 13 meters by 10 meters, and each square has side length 1 meter.