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# The diagonal distance of square A is one-half the diagonal distance ac

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Joined: 02 Sep 2009
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The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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30 Aug 2018, 04:14
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Difficulty:

5% (low)

Question Stats:

84% (01:08) correct 16% (00:49) wrong based on 58 sessions

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The diagonal distance of square A is one-half the diagonal distance across square B. What is the ratio of the area of square A to the area of square B?

A. 8 : 1
B. 2 : 1
C. 1 : 2
D. 1 : 4
E. 1 : 8

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Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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30 Aug 2018, 04:27
A x
B 2x
x/√2:2x/√2
1:2

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Joined: 07 Oct 2017
Posts: 265
Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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30 Aug 2018, 04:30
1
Bunuel wrote:
The diagonal distance of square A is one-half the diagonal distance across square B. What is the ratio of the area of square A to the area of square B?

A. 8 : 1
B. 2 : 1
C. 1 : 2
D. 1 : 4
E. 1 : 8
Attachment:

1535632314568.jpg [ 72.69 KiB | Viewed 494 times ]

Thank you = Kudos
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Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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30 Aug 2018, 04:40
Bunuel wrote:
The diagonal distance of square A is one-half the diagonal distance across square B. What is the ratio of the area of square A to the area of square B?

A. 8 : 1
B. 2 : 1
C. 1 : 2
D. 1 : 4
E. 1 : 8

Square: $$area =\frac{d^2}{2}$$ , where d is the length of either diagonal
$$\frac{area A}{area B} =\frac{\frac{dA^2}{2}}{\frac{dB^2}{2}} = \frac{dA^2}{dB^2} = (\frac{dA}{dB})^2 = (\frac{1}{2})^2 = \frac{1}{4}$$
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Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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30 Aug 2018, 08:33
Palash01675502606 wrote:
A x
B 2x
x/√2:2x/√2
1:2

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Hi Palash01675502606,
Area of square=$$a^2$$, where 'a' is the length of its side.

Square the numerator & denominator and simplify.
$$\frac{(x}{√2)^2/(2x/√2)^2}$$
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Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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04 Sep 2018, 03:46
Bunuel wrote:
The diagonal distance of square A is one-half the diagonal distance across square B. What is the ratio of the area of square A to the area of square B?

A. 8 : 1
B. 2 : 1
C. 1 : 2
D. 1 : 4
E. 1 : 8

We can let the side of square a = a and the side of square b = b. We know that the ratio of a side of a square to its diagonal is x : x√2. Thus, the diagonal of square a is a√2, and the diagonal of square b is b√2. We are given that square a’s diagonal is half that of square b. Thus, we have:

a√2 = 1/2(b√2)

2a√2 = b√2

2a = b

4a^2 = b^2

a^2/b^2 = 1/4

Alternate Solution:

We know that the length of the diagonal of a square is √2 times the length of one of its sides. Thus, if we have two squares, the ratio of the lengths of sides of these squares is the same as the ratio of the lengths of their diagonals. Furthermore, since the area of a square is found by squaring the length of a side, the ratio of the areas of two squares is the square of the ratio of the lengths of the sides. Putting these two pieces of information together, we conclude that the ratio of the areas of the squares can be found simply by squaring the ratio of the lengths of the diagonals. Since the ratio of the lengths of the diagonals is 1:2, the ratio of the areas is 1:4.

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Re: The diagonal distance of square A is one-half the diagonal distance ac  [#permalink]

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04 Sep 2018, 07:49
Bunuel wrote:
The diagonal distance of square A is one-half the diagonal distance across square B. What is the ratio of the area of square A to the area of square B?

A. 8 : 1
B. 2 : 1
C. 1 : 2
D. 1 : 4
E. 1 : 8

Let diagonal Distance of square A be $$1\sqrt{2}$$ , so sides of A are $$1$$
Let diagonal Distance of square B be $$2\sqrt{2}$$ , so sides of B are $$2$$

So, Ratio of Area of A : Ratio of Area of B is $$1^2 : 2^2 = 1 : 4$$, Answer must be (D) 1 : 4
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Re: The diagonal distance of square A is one-half the diagonal distance ac &nbs [#permalink] 04 Sep 2018, 07:49
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