Question

The area of a square is S, and that of the square formed by joining the mid-points of the given square is A. The value of `A/S` is equal to:

Options

• 0.125

• 0.25

• 1.25

• 0.5

Answer 1

0.5

Explanation:

ABCD is a square and E, F, G, H is mid-point of square ABCD.

Now, Area of square ABCD = S

Let side of square ABCD = a

∴ Area = a² = S   .......(i)

Now, In ΔEBF, EF = `sqrt((a/2)^2 + (a/2)^2) = a/sqrt(2)`

So, side of square EFGH = `a/sqrt(2)`

∴ Area = `(a/sqrt(2))^2 = a^2/2` = A  ......(ii)

Now, Value of `A/S = a^2/(2a^2)` = 0.5