Question : The ratio of the areas of two squares one having double its diagonal than the other is:
Option 1: 3 : 2
Option 2: 2 : 1
Option 3: 4 : 1
Option 4: 3 : 1
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Correct Answer: 4 : 1
Solution : Let the diagonal of the 1 st square be $2x$. Area of 1st square = $\frac{1}{2}$ × (product of diagonals) = $\frac{1}{2}×(2x)^2$ Since the diagonal of the 2 nd square is half of the diagonal of the 1 st square i.e. $x$. So, the area of 2 nd square = $\frac{1}{2}$ × (product of diagonals) = $\frac{1}{2}×x^2$ So, Area of 1 st square : Area of 2 nd square = $\frac{1}{2}×4x^2$ : $\frac{1}{2}×x^2$ = 4 : 1 Hence, the correct answer is 4 : 1.
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