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16 Sep 2014, 00:50
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Is the length of the diagonal of the rectangle greater than \(\sqrt{6}\) centimeters ?
(1) The shorter side of the rectangle measures 2 centimeters.
(2) The longer side of the rectangle measures 3 centimeters.
(1) The shorter side of the rectangle measures 2 centimeters.
(2) The longer side of the rectangle measures 3 centimeters.
16 Sep 2014, 00:50
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Official Solution:
Is the length of the diagonal of the rectangle greater than \(\sqrt{6}\) centimeters ?
(1) The shorter side of the rectangle measures 2 centimeters.
Since the length of the shorter side of the rectangle is 2 centimeters, the length of the diagonal must be greater than \(\sqrt{2^2 + 2^2} = \sqrt{8}\) centimeters. Therefore, the length of the diagonal of the rectangle is indeed greater than \(\sqrt{6}\) centimeters. Sufficient.
(2) The longer side of the rectangle measures 3 centimeters.
With the longer side of the rectangle measuring 3 centimeters, the length of the diagonal must be greater than \(\sqrt{0^2 + 3^2} = \sqrt{9}\) centimeters. Therefore, the length of the diagonal of the rectangle is also greater than \(\sqrt{6}\) centimeters. Sufficient.
Answer: D
Is the length of the diagonal of the rectangle greater than \(\sqrt{6}\) centimeters ?
(1) The shorter side of the rectangle measures 2 centimeters.
Since the length of the shorter side of the rectangle is 2 centimeters, the length of the diagonal must be greater than \(\sqrt{2^2 + 2^2} = \sqrt{8}\) centimeters. Therefore, the length of the diagonal of the rectangle is indeed greater than \(\sqrt{6}\) centimeters. Sufficient.
(2) The longer side of the rectangle measures 3 centimeters.
With the longer side of the rectangle measuring 3 centimeters, the length of the diagonal must be greater than \(\sqrt{0^2 + 3^2} = \sqrt{9}\) centimeters. Therefore, the length of the diagonal of the rectangle is also greater than \(\sqrt{6}\) centimeters. Sufficient.
Answer: D
07 May 2023, 06:44
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
