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
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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