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Question

What will be the ratio of the areas of squares, when the diagonal of one square is twice of the other.


A

1:3

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B

3:1

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C

5:1

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D

4:1

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Solution

The correct option is D

4:1


Let the length of one diagonal be x units.
The length of the other diagonal is 2x units
Applying Pythagoras theorem,
2×(side of square)2=(length of diagonal)2
(side of square)2
= 12×(length of diagonal)2
Sides of the squares will be 4x22=2x2
and x22=x2
Area of square = (side of square)2

Hence the ratio of the area of squares is (2x2)2 and (x2)2

= 12×(2x)2:12×x2
= 4: 1

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