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# The perimeter of a rectangular patio is 268 feet and its length is 168

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Math Expert
Joined: 02 Sep 2009
Posts: 48034
The perimeter of a rectangular patio is 268 feet and its length is 168  [#permalink]

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09 Jun 2018, 00:12
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Difficulty:

25% (medium)

Question Stats:

89% (01:08) correct 11% (02:08) wrong based on 57 sessions

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The perimeter of a rectangular patio is 268 feet and its length is 168% of its width. What is the area of the patio, in square feet?

(A) 4,000
(B) 4,200
(C) 4,320
(D) 4,600
(E) 4,760

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Re: The perimeter of a rectangular patio is 268 feet and its length is 168  [#permalink]

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09 Jun 2018, 00:38
Bunuel wrote:
The perimeter of a rectangular patio is 268 feet and its length is 168% of its width. What is the area of the patio, in square feet?

(A) 4,000
(B) 4,200
(C) 4,320
(D) 4,600
(E) 4,760

If the width of the rectangular patio is x, the length(which is 168% the width) is 1.68x

We know that the perimeter of the patio is 268.
$$2(x + 1.68x) = 268$$ --> $$5.36x = 268$$ --> $$x = \frac{268*100}{536} = \frac{100}{2} = 50$$

Therefore, the area of the rectangular patio is $$1.68*x^2 = 1.68*2500$$ = 4200(Option B)

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Re: The perimeter of a rectangular patio is 268 feet and its length is 168  [#permalink]

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09 Jun 2018, 01:30
Given that Perimeter of the rectangular patio is 268 feet.
Let length be L feet and breadth be B feet.
This implies 2L + 2B = 268 or L + B = 134. ---> 1
It is also given that L = 168% of W. This mean $$L =\frac{168}{100}B$$. Which can be further implied as $$\frac{L}{W} = \frac{42}{25}$$. So, L = 42k and B=25k.
Substituting in equation 1.
42k +25k = 134. =>k=2.
L = 42k = 42x2= 84.
B = 25k = 25x2 = 50.
Area of rectangle = L X B = 84 X 50 = 4200.
The correct answer is Option B.
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Re: The perimeter of a rectangular patio is 268 feet and its length is 168  [#permalink]

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09 Jun 2018, 04:58
Bunuel wrote:
The perimeter of a rectangular patio is 268 feet and its length is 168% of its width. What is the area of the patio, in square feet?

(A) 4,000
(B) 4,200
(C) 4,320
(D) 4,600
(E) 4,760

Given, 2(L+W)=268 feet
Or, 2(1.68W+W)=268
Or, 2.68W=$$\frac{268}{2}$$
Or, W=$$\frac{268}{2*2.68}$$ feet

Area of rectangular patio=L*W=1.68*$$\frac{268}{2*2.68}$$*$$\frac{268}{2*2.68}$$=$$1.68*\frac{100}{4}*\frac{100}{4}$$=4200 sq. feet

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Re: The perimeter of a rectangular patio is 268 feet and its length is 168 &nbs [#permalink] 09 Jun 2018, 04:58
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