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# A rectangular rug covers half of a rectangular floor that is 9 feet

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Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128888 [1], given: 12183

A rectangular rug covers half of a rectangular floor that is 9 feet [#permalink]

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19 Sep 2017, 23:36
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A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long
is the rug?

(A) 6
(B) 21/2
(C) 2√7
(D) 6√2
(E) 4√6
[Reveal] Spoiler: OA

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Kudos [?]: 128888 [1], given: 12183

Manager
Joined: 25 Nov 2015
Posts: 231

Kudos [?]: 64 [0], given: 240

Location: India
GPA: 3.64
WE: Engineering (Energy and Utilities)
Re: A rectangular rug covers half of a rectangular floor that is 9 feet [#permalink]

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20 Sep 2017, 12:17
Bunuel wrote:
A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long
is the rug?

(A) 6
(B) 21/2
(C) 2√7
(D) 6√2
(E) 4√6

The rug covers half of the floor i.e area of the rug = 1/2 of the rectangular floor
=12x9/2
Let the length and width of the rug be l,b respectively.
lxb=12x9/2
Since the dimensions of the rug are in the same ratio as those of the floor, $$\frac{l}{12}$$ x $$\frac{b}{9}$$ = $$\frac{1}{2}$$ which is $$\frac{1}{\sqrt{2}}$$ x $$\frac{1}{\sqrt{2}}$$
Hence, l=$$\frac{12}{\sqrt{2}}$$ = $$6\sqrt{2}$$

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Kudos [?]: 64 [0], given: 240

Director
Joined: 22 May 2016
Posts: 813

Kudos [?]: 264 [3], given: 551

A rectangular rug covers half of a rectangular floor that is 9 feet [#permalink]

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20 Sep 2017, 15:13
3
KUDOS
Bunuel wrote:
A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long
is the rug?

(A) 6
(B) 21/2
(C) 2√7
(D) 6√2
(E) 4√6

Great question. Find ratio of width to length from floor dimensions, and take 1/2 area of floor set equal to L*W to find rug length.

The dimensions of the rug are in the same ratio as the floor. Express W in terms of L (to have only variable L in the area equation). That ratio will hold for the rug.

$$\frac{W}{L}= \frac{9}{12} = \frac{3}{4}$$

$$W = \frac{3}{4}L$$

Area of floor = 12 * 9 = 108
Area of rug is half that: 54

$$L * W$$ = rug area, substitute for $$W$$
$$L * \frac{3}{4}L = 54$$
$$(\frac{3}{4})L^2 = 54$$
$$L^2 = (54)(\frac{4}{3})$$
$$L^2 = 72$$
$$L= \sqrt{72}$$
$$L = 6\sqrt{2}$$

Kudos [?]: 264 [3], given: 551

A rectangular rug covers half of a rectangular floor that is 9 feet   [#permalink] 20 Sep 2017, 15:13
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# A rectangular rug covers half of a rectangular floor that is 9 feet

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