Question : The diagonals of two squares are in the ratio of 3 : 7. What is the ratio of their areas?
Option 1: 3 : 7
Option 2: 9 : 49
Option 3: 4 : 7
Option 4: 7 : 3
Correct Answer: 9 : 49
Solution :
The area (A) of a square can be expressed in terms of its diagonal by,
$A = \frac{d^2}{2}$
If the diagonals of two squares are in the ratio 3 : 7.
The ratio of their areas will be the square of the ratio of their diagonals,
$=\left(\frac{3}{7}\right)^2 = \frac{9}{49}$
Hence, the correct answer is 9 : 49.
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