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If a square region has area x, what is the length of the diagonal of

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carcass
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If a square region has area x, what is the length of the diagonal of [#permalink] New post   28 May 2017, 04:01
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If a square region has area x, what is the length of its diagonal in terms of x ?

A) \(\sqrt{x}\)

B) \(\sqrt{2x}\)

C) \(2 \sqrt{x}\)

D) \(x \sqrt{2}\)

E) \(2x\)
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Bunuel
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Re: If a square region has area x, what is the length of the diagonal of [#permalink] New post   09 Apr 2018, 02:05
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dave13 wrote:
Bunuel wrote:
carcass wrote:
If a square region has area x, what is the length of its diagonal in terms of x ?

A) \(\sqrt{x}\)

B) \(\sqrt{2x}\)

C) \(2 \sqrt{x}\)

D) \(x \sqrt{2}\)

E) \(2x\)


Are of a square = \(\frac{diagonal^2}{2}\).

Given: \(\frac{diagonal^2}{2}=x\);

\(diagonal=\sqrt{2x}\).

Answer: B.


Hello Bunuel :) isnt the formula of the area of square \(a^2\) where \(a\) is side of square ? :?

is it another formula ? \(\frac{diagonal^2}{2}\). does diagonal of square mean \(a\sqrt{2}\) :? cause you write so \(diagonal^2\)

have a great monday :)


Yes, the area of a square could also be found by \(\frac{diagonal^2}{2}\).
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Re: If a square region has area x, what is the length of the diagonal of [#permalink] New post   28 May 2017, 04:07
B as the diagonal of a square with side a is sqrt(2) * a. Here a is sqrt(x)

answer will be sqrt(2x)


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Re: If a square region has area x, what is the length of the diagonal of [#permalink] New post   28 May 2017, 04:13
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carcass wrote:
If a square region has area x, what is the length of its diagonal in terms of x ?

A) \(\sqrt{x}\)

B) \(\sqrt{2x}\)

C) \(2 \sqrt{x}\)

D) \(x \sqrt{2}\)

E) \(2x\)


Are of a square = \(\frac{diagonal^2}{2}\).

Given: \(\frac{diagonal^2}{2}=x\);

\(diagonal=\sqrt{2x}\).

Answer: B.
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If a square region has area x, what is the length of its diagonal in [#permalink] New post   27 Sep 2017, 05:56
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Bunuel wrote:
If a square region has area x, what is the length of its diagonal in terms of x?

(A) √x
(B) √(2x)
(C) 2√x
(D) x√2
(E) 2x

Because \(s^2\) = area of a square:

\(s^2 = x\)
\(s = \sqrt{x}\)

A square's diagonal* is given by \(s\sqrt{2}\)

\(\sqrt{x} * \sqrt{2} = \sqrt{2x}\)

Answer B

*OR use Pythagorean theorem, where hypotenuse = diagonal = d

\((\sqrt{x})^2 + (\sqrt{x})^2 = d^2\)
\(2x = d^2\)
\(\sqrt{2x} = \sqrt{d^2}\)
\(d =\sqrt{2x}\)
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Re: If a square region has area x, what is the length of the diagonal of [#permalink] New post   09 Apr 2018, 02:01
Bunuel wrote:
carcass wrote:
If a square region has area x, what is the length of its diagonal in terms of x ?

A) \(\sqrt{x}\)

B) \(\sqrt{2x}\)

C) \(2 \sqrt{x}\)

D) \(x \sqrt{2}\)

E) \(2x\)


Are of a square = \(\frac{diagonal^2}{2}\).

Given: \(\frac{diagonal^2}{2}=x\);

\(diagonal=\sqrt{2x}\).

Answer: B.


Hello Bunuel :) isnt the formula of the area of square \(a^2\) where \(a\) is side of square ? :?

is it another formula ? \(\frac{diagonal^2}{2}\). does diagonal of square mean \(a\sqrt{2}\) :? cause you write so \(diagonal^2\)

have a great monday :)
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Re: If a square region has area x, what is the length of the diagonal of [#permalink] New post   13 May 2021, 21:51
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Re: If a square region has area x, what is the length of the diagonal of [#permalink]
13 May 2021, 21:51
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