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# What is the longest straight line that can be inscribed in a

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What is the longest straight line that can be inscribed in a [#permalink]

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21 May 2013, 02:09
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What is the longest straight line that can be inscribed in a rectangle with a perimeter of 16 and sides of integer length?

A. 4 root 2
B. 6
C. 7
D. 5 root 2
E. 7 root 2

[Reveal] Spoiler: OA

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Re: What is the longest straight line that can be inscribed in a [#permalink]

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21 May 2013, 02:18
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fozzzy wrote:
What is the longest straight line that can be inscribed in a rectangle with a perimeter of 16 and sides of integer length?

A. 4 root 2
B. 6
C. 7
D. 5 root 2
E. 7 root 2

Basically we are asked to maximize the length of the diagonal in a rectangle with a perimeter of 16.

Say a and b are the lengths of the sides, then we have that 2a + 2b = 16 --> a + b = 8.

We need to maximize $$d=\sqrt{a^2+b^2}$$. Since a and b are integers then $$d_{max}$$ is obtained when a=1 and b=7 or vise-versa (by trial and error) --> $$d=\sqrt{a^2+b^2}=\sqrt{50}=5\sqrt{2}$$.

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Re: What is the longest straight line that can be inscribed in a [#permalink]

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21 May 2013, 02:24
Longest straight line that can be inscribed in a rectangle = the diagonal of that rectangle.
Longest diagonal can be obtained when one side of the rectangle has shortest possible length and the other side has the longest possible length when perimeter is constant.

In this case, as the sides are integers, shortest side can be 1 and longest side can be 7.

Then, diagonal of the rectangle = $$\sqrt{(1^2 + 7^2)} = \sqrt{50} = 5\sqrt{2}$$

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Re: What is the longest straight line that can be inscribed in a [#permalink]

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15 Sep 2014, 09:57
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Re: What is the longest straight line that can be inscribed in a [#permalink]

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28 Mar 2016, 10:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the longest straight line that can be inscribed in a   [#permalink] 28 Mar 2016, 10:28
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