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If a square has a side of length s and a diagonal of length d, then s2

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If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 04 Oct 2017, 00:41
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Re: If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 04 Oct 2017, 00:56
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Bunuel wrote:
If a square has a side of length s and a diagonal of length d, then s^2/d^2 =

(A) 1/4
(B) √2/4
(C) 1/2
(D) √2/2
(E) 2/1



Diagonal d of a square = \(s\sqrt{2}\)

Therefore, s^2/d^2 = s^2/(\((s\sqrt{2}\))^2 = 1/2

Answer : C

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Re: If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 04 Oct 2017, 04:55
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diag=root 2
d= root 2*2
s^2/ d^2== 1/2

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Re: If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 04 Oct 2017, 09:17
Diagonal d of a square = s2√s2

Therefore, s^2/d^2 = s^2/((s2√(s2)^2 = 1/2

Answer : C

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If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 04 Oct 2017, 11:43
Bunuel wrote:
If a square has a side of length s and a diagonal of length d, then s^2/d^2 =

(A) 1/4
(B) √2/4
(C) 1/2
(D) √2/2
(E) 2/1

Another way is to choose numbers.

Let \(s = 2\), then \(d = s \sqrt{2}\), so
\(d = 2\sqrt{2}\)

\(\frac{s^2}{d^2}\) = \(\frac{2^2}{(2\sqrt{2})^2}\) = \(\frac{4}{8} = \frac{1}{2}\)

Answer C

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Re: If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 06 Oct 2017, 10:52
Bunuel wrote:
If a square has a side of length s and a diagonal of length d, then s^2/d^2 =

(A) 1/4
(B) √2/4
(C) 1/2
(D) √2/2
(E) 2/1


We may recall that diagonal = side√2; thus:

d = s√2

s/d = 1/√2

s^2/d^2 = (1/√2)^2 = 1/2

Answer: C
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Re: If a square has a side of length s and a diagonal of length d, then s2 [#permalink]

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New post 06 Oct 2017, 21:07
In case you can't recall the direct formula, start with the Pythagoras theorem:

a^2 + b^2 = c^2, where a and b are sides of a right-angled triangle and c is the hypotenuse.

For a square, since all sides are equal, you get

s^2 + s^2 = d^2

And then the solution is as mentioned above by others.

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Re: If a square has a side of length s and a diagonal of length d, then s2   [#permalink] 06 Oct 2017, 21:07
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