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# The length (in feet) of a rectangle is 4 more than twice its width. Th

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Math Expert
Joined: 02 Sep 2009
Posts: 44645
The length (in feet) of a rectangle is 4 more than twice its width. Th [#permalink]

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29 Mar 2018, 00:45
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Question Stats:

76% (01:00) correct 24% (01:24) wrong based on 29 sessions

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The length (in feet) of a rectangle is 4 more than twice its width. The area of the rectangle is 70 feet^2. What is the length (in feet) of the rectangle?

(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
[Reveal] Spoiler: OA

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Joined: 16 Sep 2016
Posts: 209
WE: Analyst (Health Care)
Re: The length (in feet) of a rectangle is 4 more than twice its width. Th [#permalink]

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29 Mar 2018, 00:53
Bunuel wrote:
The length (in feet) of a rectangle is 4 more than twice its width. The area of the rectangle is 70 feet^2. What is the length (in feet) of the rectangle?

(A) 5
(B) 7
(C) 10
(D) 12
(E) 14

Area of rectangle is length * width.

Let the length be L.
It is given to be 2*W + 4 , where W is width.
$$L = 2W+4$$
$$W = (L-4)/2$$

$$L*W = 70$$
$$L*(L-4)/2 = 70$$ ...(Substitute W in)
$$L^2 - 4L - 140 = 0$$

140 = 7*2*2*5 ... hence 14*10 we can use this to factorize...

$$L^2 - 14L + 10L - 140 = 0$$
$$L (L- 14)+ 10(L - 14) = 0$$
$$(L + 10)(L - 14) = 0$$
L= +14, -10 ... since L >0
$$L=14$$

Hence Option (E) is correct.

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Joined: 22 May 2016
Posts: 1561
The length (in feet) of a rectangle is 4 more than twice its width. Th [#permalink]

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29 Mar 2018, 19:30
Bunuel wrote:
The length (in feet) of a rectangle is 4 more than twice its width. The area of the rectangle is 70 feet^2. What is the length (in feet) of the rectangle?

(A) 5
(B) 7
(C) 10
(D) 12
(E) 14

$$l * w = Area, A$$
$$l= 2w + 4$$
$$A = 70$$
$$(2w + 4) * w = 70$$
$$2w^2 + 4w - 70 = 0$$
$$w^2 + 2w - 35=0$$
$$(w + 7)(w - 5) = 0$$
$$w = 5$$ (length cannot be negative)
$$l = (2w + 4) = (10 + 4) = 14$$

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The length (in feet) of a rectangle is 4 more than twice its width. Th   [#permalink] 29 Mar 2018, 19:30
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