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The Diagonals of two squares are in the ratio of 2:5. find the ratio of their areas.

A. $4 : 15$

B. $4 : 25$

C. $3 : 15$

D. $3 : 25$

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Correct Answer :

B. $4 : 25$

Let the diagonals of the squares be 2x and 5x.
Then ratio of their areas will be

A r e a o f s q u a r e = \frac{1}{2} * D i a g o n a l^{2} \frac{1}{2} * 2 x^{2} : \frac{1}{2} * 5 x^{2} 4 x^{2} : 25 x^{2} = 4 : 25

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