In the figure shown, the outer square has an area of
9 cm2, the inner square has an area of 1 cm2, and the
four rectangles are identical. What is the perimeter of
one of the four identical rectangles?
Options
A) 6 cm B) 8 cm C) 10 cm D) 9 cm E) 7 cm
The outer square has an area of 9 cm2, so the sides of this outer   square have length 3 cm (since 3 3 = 9), and thus PN = 3 cm.   The inner square has an area of 1 cm2, so the sides of this inner   square have length 1 cm (since 1 1 = 1), and thus MR = 1 cm.   Since PN = 3 cm, then PS + SN = 3 cm and so QR + SN = 3 cm   (since QR = PS).   But QR = QM + MR, so then QM + MR + SN = 3 cm or   QM + 1 + SN = 3 cm (since MR = 1 cm).   From this last equation we get QM + SN = 2 cm.   P Q   R   S   M   N   Since each of QM and SN is the width of an identical rectangle, then QM = SN = 1 cm.   Using PS + SN = 3 cm, we get PS + 1 = 3 cm and so PS = 2 cm.   Since the rectangles are identical, then SN = PQ = 1 cm.   The perimeter of rectangle PQRS is 2 (PS + PQ) = 2x(2 + 1) = 2x3 = 6 cm.   correct answer 6 cm
<result>A</result>
In the figure shown, the outer square has an area of
9 cm2, the inner square has an area of 1 cm2, and the
four rectangles are identical. What is the perimeter of
one of the four identical rectangles?