I saw this one posted not too long ago. Lemme see if I can do this correctly.
As you say, the diagonals of the squares show that the rectangle's L:W ratio is 2:1. That means you can solve it so that L = 2W.
Since the perimeter is 18SQRT2, that means
2L + 2W = 18SQRT2
2(2W) + 2W = 18SQRT2
4W + 2W = 18SQRT2
6W = 18SQRT2
W = 3SQRT2
W is equal to the diagonal of the squares. If you know the diagonal of one square, you can find out the length of its side.
If diagonal of a square is 3SQRT2, then the side is 3, since a side of a square is diagonal/SQRT2 -- (This is because a diagonal inside a square makes a 90-45-45 isosceles right triangle - you can use Pythagoreans theorem to prove this)
So if one side of a square is 3, then perimeter of square is 4*3 = 12. Answer choice B.
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ps question
Source: Beat The GMAT — Problem Solving |
First, you should realize that the small side of the rectangle is half of the long side.
This is b/c of the 2 inscribed squares.
Therefore, you get: 6x=18sqrt(2)
x=3sqrt(2)
Then, the diagonal of the squares is also 3sqrt(2).
So, a side of the square is 3, b/c the diagonal forms a 45, 45, 90 triangle.
Finally, 3*4=12.
Perimeter equals 12.
This is b/c of the 2 inscribed squares.
Therefore, you get: 6x=18sqrt(2)
x=3sqrt(2)
Then, the diagonal of the squares is also 3sqrt(2).
So, a side of the square is 3, b/c the diagonal forms a 45, 45, 90 triangle.
Finally, 3*4=12.
Perimeter equals 12.
