alltimeacheiver wrote:In the figure shown above, two identical squares are inscribed in the rectangle. If the perimeter of the rectangle is 18 by squareroot2, then what is the perimeter of each square?
(A) 8 by squareroot2
(B) 12
(C) 12 by squareroot2
(D) 16
(E) 18
The figure looks like in the attached image.
Perimeter = 18 × √2, which implies 2 × (length + width) = 18√2
or Length + Width = 9√2
Let side of square = a implies diagonal of the square = a√2
Now, length of rectangle = 2 × diagonal of square = 2a√2
width of rectangle = diagonal of square = a√2
Length + Width = 9√2 implies 2a√2 + a√2 = 9√2
3a√2 = 9√2 or a = 3 or side of the square = 3
So, perimeter of the square = 3 × 4 = 12
The correct answer is B.
