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# Which of the following expresses the length of the greatest distance

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Math Expert
Joined: 02 Sep 2009
Posts: 54376
Which of the following expresses the length of the greatest distance  [#permalink]

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06 Jun 2017, 11:35
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Difficulty:

45% (medium)

Question Stats:

51% (00:57) correct 49% (00:38) wrong based on 111 sessions

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Which of the following expresses the length of the greatest distance between any two points on a square with area a?

A. a
B. √a
C. a√2
D. √(2a)
E. 2√a

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Posts: 331
Re: Which of the following expresses the length of the greatest distance  [#permalink]

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06 Jun 2017, 13:27
greatest distance between any two points on a square will be the two opposite ends of the diagonal.

Area of the square = a
Side of the square = √a
Diagonal = $$\sqrt{2* (√a)^2}$$ = a√2

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Re: Which of the following expresses the length of the greatest distance  [#permalink]

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06 Jun 2017, 21:55
quantumliner wrote:
greatest distance between any two points on a square will be the two opposite ends of the diagonal.

Area of the square = a
Side of the square = √a
Diagonal = $$\sqrt{2* (√a)^2}$$ = a√2

Should be D.
The length of the diagonal for a square is $$\sqrt{2}*Side$$

Side = $$\sqrt{a}$$
Thus, diagonal should be $$\sqrt{2a}$$
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Re: Which of the following expresses the length of the greatest distance  [#permalink]

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10 Jun 2017, 07:35
Bunuel wrote:
Which of the following expresses the length of the greatest distance between any two points on a square with area a?

A. a
B. √a
C. a√2
D. √(2a)
E. 2√a

Recall that the greatest distance between any two points on a square is its diagonal and that the diagonal of a square is s√2, where s = side of the square.

Since the area of the square is a and area = s^2, we have a = s^2, or s = √a.

Thus, the diagonal of the square = (√a)(√2) = √(2a).

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Re: Which of the following expresses the length of the greatest distance  [#permalink]

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11 Jun 2017, 12:48
Bunuel wrote:
Which of the following expresses the length of the greatest distance between any two points on a square with area a?

A. a
B. √a
C. a√2
D. √(2a)
E. 2√a

Let us assume a=64,so side of square be 8.
Diagonal will be sq. root of (8^2+8^2)=sq. root of (64+64)=sq. root of 2a
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Re: Which of the following expresses the length of the greatest distance  [#permalink]

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02 Jul 2017, 09:02
very easy question, but we need to solve this with little caution. i got the wrong answer in 30 seconds.

here area of the square is given as 'a'.
i did not notice it n considered area as a^2 and got D as the answer.
Re: Which of the following expresses the length of the greatest distance   [#permalink] 02 Jul 2017, 09:02
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