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The object of this brain builder is to find the value of "x".

The picture is made up entirely of SQUARES.
The perimeter of the small white square is "4x".The area of the entire outer rectangle is 6,426 square units.

Good luck.

the value of "x" is____________



Click HERE to check your answer.


If you got the correct answer the first time without looking, you are good.

So try these two variations:

  1. Find the value of "x" if the perimeter of the white square is 4x + 4 and the large rectangular area is 25,704 square units.
  2. Find the length and width of the large rectangle if the white square is 2x + 3 units long and the total perimeter is 770 units.


Click to see if you were correct.


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The value of x is 3.

Here is a bit of help to get you started toward the answer.

If the perimeter of the small square is "4x", then the length of its side is "x", and its area is x^2.

So the area of the red square is also x^2.

Now the side of the yellow square is 2x, and its area is then 4x^2.

This makes the side of the green square 3x, and its area is

Continue in this manner to find the areas of each square, then add them together and set the sum equal to 6,426 and solve for "x".

Or perhaps you can think of another way......

Back to try some more.


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Variation answers:

1.) x = 5

2.) length = 238 units, width = 147 units



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