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# If the ratio of the areas of two squares is 2 : 1, then the ratio of

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If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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02 Nov 2017, 01:27
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If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1
[Reveal] Spoiler: OA

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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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02 Nov 2017, 07:33
Area= side^2

so Side1/side2=sqrt2/1

perimeter=4Side

Perimiter1/perimter2 = Sqrt2/1
c

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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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02 Nov 2017, 08:13
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Bunuel wrote:
If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1

Sides of the square are in the ratio $$\sqrt{2} : 1$$

Ratio of Perimeter will be same as the ratio of the sides of the square , ie $$\sqrt{2} : 1$$, answer will be (C)
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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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02 Nov 2017, 08:30
Bunuel wrote:
If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1

From the area formula for a square $$s^2$$, the ratio of the areas = $$2s^2/s^2$$.

Rather than working with the algebra to find the ratio of the perimeters, it is possible to just plug in an easy value for s, or the side length of the small square, such as s = 2.

If s = 2, then the area of the big square is $$2s^2 = 8$$ and the area of the small square is $$s^2 = 4$$.

Now, solve for the side of the big square by square rooting each side of the equation $$s^2 = 8$$, to find that for the big square $$s = 2\sqrt{2}$$

Lastly, recognize that since each side value is simply multiplied by 4 to find perimeter we can just set the sides in a ratio to each other to find the ratio of the perimeters such as $$2\sqrt{2}/2$$ which simplifies to $$\sqrt{2}/1$$.

The correct answer is choice C.
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If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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02 Nov 2017, 08:49
Bunuel wrote:
If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1

Choose values
Let the smaller square, A, have side = 1
Area = s$$^2 = 1^2 = 1$$

Let the area of the larger square, B, = 2, to conform to the given ratio of areas as 2:1

The side length of B:
Area = s$$^2$$
2 = s$$^2$$
$$s =\sqrt{2}$$

Ratio of perimeters? A square has four equal sides. The ratio of (side B): (side A) is the same whether you use all four sides or just one. Side B = $$\sqrt{2}$$. Side A = $$1$$

Ratio of perimeters, $$\frac{sideB}{sideA}=\frac{\sqrt{2}}{1}$$

Scale factor
Scale factor is the amount by which each length in square A has been increased. (Length * length = area)

To enlarge area of A to B, the scale factor $$k$$ was squared.

Square B = $$(\frac{b}{a})^2 = k^2$$, where b = side length of B and a = side length of A.

Area of B is two times that of A. The scale factor to get the increase in size was $$k^2 =(\frac{2}{1})$$

To get back to one-dimensional length, i.e., ratio of perimeters $$\frac{b}{a}$$:

Scaled down, B to A = $$\sqrt{k^2}$$=$$\frac{\sqrt{2}}{\sqrt{1}}$$=$$\frac{\sqrt{2}}{1}$$

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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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05 Nov 2017, 07:26
Bunuel wrote:
If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1

We can let n = the side length of the smaller square and m = the side length of the larger square; thus:

m^2/n^2 = 2/1

The ratio of the sides of the squares is:

m/n = √2/1

The perimeter of a square is 4 times its side; thus, the ratio of the perimeters of the two squares is 4√2/4 = √2/1.

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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of [#permalink]

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05 Nov 2017, 08:53
Bunuel wrote:
If the ratio of the areas of two squares is 2 : 1, then the ratio of the perimeters of the squares is

(A) 1 : 2

(B) $$1 :\sqrt{2}$$

(C) $$\sqrt{2}: 1$$

(D) 2 : 1

(E) 4 : 1

let square one area=8; side=2√2; perimeter=8√2
let square two area=4; side=2; perimeter=8
8√2:8=√2:1
C

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Re: If the ratio of the areas of two squares is 2 : 1, then the ratio of   [#permalink] 05 Nov 2017, 08:53
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