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If square A B C D has area 25 , and the area of the larger
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31 May 2026, 06:51
31 May 2026, 06:51
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Question Stats:
75% (02:20) correct
25% (01:21) wrong based on 12 sessions
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If square \(A B C D\) has area 25 , and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?
Note: Figure not drawn to scale
GRe If square A B C D has area 25 , and the area of the larger.png [ 32.42 KiB | Viewed 470 times ]
\(\begin{aligned}
& A. 3 / 4 \\
& B. 5 / 4 \\
& C. 6 / 5 \\
& D. 4 / 3 \\
& E. 5 / 3
\end{aligned}\)
Note: Figure not drawn to scale
Attachment:
GRe If square A B C D has area 25 , and the area of the larger.png [ 32.42 KiB | Viewed 470 times ]
\(\begin{aligned}
& A. 3 / 4 \\
& B. 5 / 4 \\
& C. 6 / 5 \\
& D. 4 / 3 \\
& E. 5 / 3
\end{aligned}\)
- Part of the project: GRE Daily Quant Challenge - Topic-Wise 2025!!!
- Also replying to the unanswered questions
If square A B C D has area 25 , and the area of the larger
[#permalink]
01 Jun 2026, 03:38
01 Jun 2026, 03:38
1
Carcass wrote:
If square \(A B C D\) has area 25 , and the area of the larger shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?
Note: Figure not drawn to scale
\(\begin{aligned}
& A. 3 / 4 \\
& B. 5 / 4 \\
& C. 6 / 5 \\
& D. 4 / 3 \\
& E. 5 / 3
\end{aligned}\)
Note: Figure not drawn to scale
Attachment:
GRe If square A B C D has area 25 , and the area of the larger.png
\(\begin{aligned}
& A. 3 / 4 \\
& B. 5 / 4 \\
& C. 6 / 5 \\
& D. 4 / 3 \\
& E. 5 / 3
\end{aligned}\)
Square ABCD has side lengths of \(\sqrt{25}=5\).
Let the smaller shaded square have side length \(x\) and the larger shaded sqaure have side length \(5-x\), so we can set up the following equation:
\(9x^2=(5-x)^2\)
\(9x^2=25-10x+x^2\)
\(8x^2+10x-25=0\)
\((4x-5)(2x+5)=0\)
Since we are talking about positve lengths, \(x>0\), we get \(x=\frac{5}{4}\).
Answer: B) \(\frac{5}{4}\)
gmatclubot
If square A B C D has area 25 , and the area of the larger [#permalink]
01 Jun 2026, 03:38
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