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 valuesLet 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, \(\frac{sideB}{sideA}=\frac{\sqrt{2}}{1}\)

Answer C

Scale factorScale 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 = \(\sqrt{k^2}\)=\(\frac{\sqrt{2}}{\sqrt{1}}\)=\(\frac{\sqrt{2}}{1}\)

Answer C

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The only thing more dangerous than ignorance is arrogance.

-- Albert Einstein