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Twice the length of the diagonal of the same rectangle

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Twice the length of the diagonal of the same rectangle [#permalink] New post   26 Oct 2022, 01:12
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Quantity A
Quantity B
The perimeter of a rectangle
Twice the length of the diagonal of the same rectangle



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


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SaquibHGREWhiz
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Twice the length of the diagonal of the same rectangle [#permalink] New post   26 Oct 2022, 21:38
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Let's say the length is L and the width is W.

So the perimeter = 2(L + W)
And the double of the diagonal = \(2 × \sqrt{L^2 + W^2}\)

So we are comparing L + W and \(\sqrt{L^2 + W^2}\)

We can visualize a right-angle triangle here where \(\sqrt{L^2 + W^2}\) is the diagonal (one side) and L + W is the sum of the other two sides.
    Hence L + W must be greater.

The answer is A.
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Re: Twice the length of the diagonal of the same rectangle [#permalink] New post   19 Sep 2024, 01:14
Hello from the GRE Prep Club BumpBot!

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Re: Twice the length of the diagonal of the same rectangle [#permalink]
19 Sep 2024, 01:14
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