Bunuel wrote:

In the figure above, PQRS and PRTU are squares. The ratio (perimeter of PQRS/(perimeter of PRTU) =

(A) 1/√2

(B) 1/2

(C) 2/3

(D) 3/√2

(E) 1/4

Attachment:

2017-09-29_1044_001.png

Assign numbersSide and perimeter of large square PRTULet one side of large square PRTU =\(2\)

Perimeter of PRTU =\(4s\) = \((4)(2)\) =

8Side and perimeter of small square PQRSOne side of the large square PRTU is the diagonal of the square PQRS, \(d = 2\)

Side** of small square PQRS is \(\frac{d}{\sqrt{2}}\)

\(s\) = \(\frac{2}{\sqrt{2}}\)

Perimeter of PQRS is \(4s\)= \((4)(\frac{2}{\sqrt{2}})\) =

\(\frac{8}{\sqrt{2}}\)RATIO?Ratio of (perimeter of PQRS)/(perimeter of PRTU)?

\(\frac{\frac{8}{\sqrt{2}}}{8}\) = \((\frac{8}{\sqrt{2}} * \frac{1}{8})\) =

\(\frac{1}{\sqrt{2}}\)

ANSWER A

AlgebraicallySide and perimeter of large square PRTULet side of PRTU = \(x\)

Perimeter of PRTU = \(4s\) =

4xSide and perimeter of small square PQRSOne side of PRTU is the diagonal of square PQRS, \(d = x\)

\(s = \frac{d}{\sqrt{2}}\)

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

Perimeter of PQRS = \(4s\)

Perimeter of PQRS = \((4)(\frac{x}{\sqrt{2}})\) =

\(\frac{4x}{\sqrt{2}}\)RATIO?Ratio of (perimeter of PQRS)/(perimeter of PRTU)?

\(\frac{\frac{4x}{\sqrt{2}}}{4x}\) = \((\frac{4x}{\sqrt{2}} * \frac{1}{4x})\) =

\(\frac{1}{\sqrt{2}}\)

Answer A

**

\(s\sqrt{2}= d\)

\(s =\frac{d}{\sqrt{2}}\)

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