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# A tailor trims 4 feet form opposite edges of a square piece of cloth

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Math Expert
Joined: 02 Sep 2009
Posts: 54493
A tailor trims 4 feet form opposite edges of a square piece of cloth  [#permalink]

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18 Nov 2015, 23:50
2
5
00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:33) correct 25% (02:58) wrong based on 121 sessions

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A tailor trims 4 feet form opposite edges of a square piece of cloth, and 5 feet form the other two edges. If 120 square feet of cloth remain, what was the length of a side of the original piece of cloth?

A. 12
B. 20
C. 24
D. 26
E. 40

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Re: A tailor trims 4 feet form opposite edges of a square piece of cloth  [#permalink]

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19 Nov 2015, 00:52
2
Let the current sides of rectangle be x and y
Area of rectangle = 120
=> xy = 120

Since the original lengths are equal and 8 feet and 10 feet were trimmed .
x+10= y +8
=> x = y-2

Therefore (y-2)*y= 120
=> y^2 - 2y -120 = 0
=> y = 12 ,-10
Therefore y = 12
Original length = 12+8 = 20

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Re: A tailor trims 4 feet form opposite edges of a square piece of cloth  [#permalink]

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29 Nov 2015, 12:32
1
1
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that the dimensions of a SQUARE piece of cloth are reduced by 4 feet on each of one pair of sides and 5 feet on each of the other pair of sides. This results in a total area of 120 square feet. We're asked for one of the dimensions of the ORIGINAL square cloth..

With the information given, we're reducing the dimension by 8 feet and 10 feet respectively. To end up with 120 square feet, we'll likely need an answer in the 20s.

Answer C: 24 feet

Removing the 8 feet and 10 feet, we'd end up with dimensions of 16 and 14..
(16)(14) = 224 which is TOO BIG.
Eliminate C, D and E.

While the likely answer is 20, we should confirm it to be sure...

Answer B: 20 feet

Removing the 8 feet and 10 feet, we'd end up with dimensions of 12 and 10..
(12)(10) = 120 which is an exact MATCH for what we were told, so this MUST be the answer.

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A tailor trims 4 feet form opposite edges of a square piece of cloth  [#permalink]

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18 Jul 2017, 14:24
The stimulus info yields: (x-10) (x-8) = 120. Before expanding, notice that the factors have a difference of 2, i.e. only 10 x 12 = 120 works. (This saves you at least 45 sec). Now pick a factor, say 10. Original side is either 10 + 8 = 18 (not given) or 10 + 10 = 20 (choice B).
A tailor trims 4 feet form opposite edges of a square piece of cloth   [#permalink] 18 Jul 2017, 14:24
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# A tailor trims 4 feet form opposite edges of a square piece of cloth

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