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# In the figure above, PQRS and PRTU are squares. The ratio (perimeter

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In the figure above, PQRS and PRTU are squares. The ratio (perimeter  [#permalink]

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29 Sep 2017, 00:02
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89% (01:10) correct 11% (01:46) wrong based on 35 sessions

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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 [ 5.59 KiB | Viewed 886 times ]

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Re: In the figure above, PQRS and PRTU are squares. The ratio (perimeter  [#permalink]

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29 Sep 2017, 00:07
Let PQ = a
then PR = a* [quote]√2[quote] ( take PQR as right angled triangle)

perimeter of PQRS = 4a
perimeter of PRTU = 4*a*√2
ratio = 4a/4*a*√2 = 1/√2
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In the figure above, PQRS and PRTU are squares. The ratio (perimeter  [#permalink]

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29 Sep 2017, 11:33
1

From the figure, since PQRS's diagonal is the side of the square PRTU.

We could assume the side of PQRS to be 1, making its perimeter 4,
and the diagonal of the square PQRS $$√2$$

If the diagonal is the side of the square PRTU, the perimeter is 4$$√2$$

Therefore, the ratio of perimeters of Square PQRS to PRTU is $$\frac{4}{4√2} = \frac{1}{√2}$$(Option A)
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Re: In the figure above, PQRS and PRTU are squares. The ratio (perimeter  [#permalink]

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29 Sep 2017, 16:52
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 numbers

Side and perimeter of large square PRTU

Let one side of large square PRTU =$$2$$
Perimeter of PRTU =$$4s$$ = $$(4)(2)$$ = 8

Side and perimeter of small square PQRS

One 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)?

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

$$\frac{1}{\sqrt{2}}$$

Algebraically

Side and perimeter of large square PRTU

Let side of PRTU = $$x$$
Perimeter of PRTU = $$4s$$ = 4x

Side and perimeter of small square PQRS

One 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)?

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

$$\frac{1}{\sqrt{2}}$$

**
$$s\sqrt{2}= d$$

$$s =\frac{d}{\sqrt{2}}$$
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Re: In the figure above, PQRS and PRTU are squares. The ratio (perimeter &nbs [#permalink] 29 Sep 2017, 16:52
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