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Four squares of equal sides are adjoined along the sides of a simila
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26 Jan 2025, 14:42
26 Jan 2025, 14:42
Expert Reply
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Question Stats:
50% (04:25) correct
50% (01:30) wrong based on 2 sessions
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Four squares of equal sides are adjoined along the sides of a similar square as shown in the figure above. The centers of the adjoining squares are joined to give another square. The area of the new square formed is what percent more than the area of each of the adjoining squares?
A. 20%
B. 50%
C. 75%
D. 80%
E. 100%
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Four squares of equal sides are adjoined along the sides of a simila
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03 Mar 2025, 09:37
03 Mar 2025, 09:37
Expert Reply
\(\text { Let the length of the side of each of the five similar squares be ' } x \text { ' each. }\)
Now the square formed by joining the centre's of the four similar squares has side equal to the diagonal of one of the identical square i.e. $\(\mathrm{x} \sqrt{2}\)$ (Diagonal in a square is $\(\sqrt{2}\)$ times the side)
So, the area of each of the five identical squares and that of the square formed by joining the centers of the small squares is $\(x^2 \&(x \sqrt{2})^2=2 x^2\)$ respectively. (The area of square is (side) $\({ }^2\)$ ).
Finally the area of the new square formed is $\(\frac{2 x^2-x^2}{x^2} \times 100=100 \%\)$ more than that of each of the smaller (identical) squares.
Note: - As the area of the new square is 2 times that of the smaller squares, it is obviously $100 \%$ more.
Hence the answer is (E).
Now the square formed by joining the centre's of the four similar squares has side equal to the diagonal of one of the identical square i.e. $\(\mathrm{x} \sqrt{2}\)$ (Diagonal in a square is $\(\sqrt{2}\)$ times the side)
So, the area of each of the five identical squares and that of the square formed by joining the centers of the small squares is $\(x^2 \&(x \sqrt{2})^2=2 x^2\)$ respectively. (The area of square is (side) $\({ }^2\)$ ).
Finally the area of the new square formed is $\(\frac{2 x^2-x^2}{x^2} \times 100=100 \%\)$ more than that of each of the smaller (identical) squares.
Note: - As the area of the new square is 2 times that of the smaller squares, it is obviously $100 \%$ more.
Hence the answer is (E).
gmatclubot
Four squares of equal sides are adjoined along the sides of a simila [#permalink]
03 Mar 2025, 09:37
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