Question

In the given figure, EFGH is formed by joining midpoints of consecutive sides of square ABCD. Figures PQRS and KLMN are also formed similarly. KLMN : ABCD is

• A. 1 : 4
• B. 1 : 8
• C. 1 : 16
• D. None of the above

Answer 1

The correct option is B 1 : 8

If area of KLMN = A, Areas of outer squares are each two times the inner pne's (as every time the side because $\frac{1}{\sqrt{2}}$ times) hence Area of ABCD $=2\times 2\times 2\times A=8A$
So the ratio is 1 : 8