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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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Math Expert
Joined: 02 Sep 2009
Posts: 49251
If a square has a side of length s and a diagonal of length d, then s2  [#permalink]

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04 Oct 2017, 00:41
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Question Stats:

93% (00:28) correct 7% (00:19) wrong based on 60 sessions

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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

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Joined: 17 Apr 2017
Posts: 12
Re: If a square has a side of length s and a diagonal of length d, then s2  [#permalink]

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04 Oct 2017, 00:56
1
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

Intern
Joined: 11 Mar 2014
Posts: 29
Schools: HEC Montreal '20
Re: If a square has a side of length s and a diagonal of length d, then s2  [#permalink]

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04 Oct 2017, 04:55
1
diag=root 2
d= root 2*2
s^2/ d^2== 1/2
Intern
Joined: 11 Apr 2017
Posts: 38
Schools: Kelley '20
Re: If a square has a side of length s and a diagonal of length d, then s2  [#permalink]

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

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

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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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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
$$d = 2\sqrt{2}$$

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

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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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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

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Joined: 28 May 2017
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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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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 &nbs [#permalink] 06 Oct 2017, 21:07
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