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# Rectangular floors having perimeter of 16 meters are to be covered wit

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Math Expert
Joined: 02 Sep 2009
Posts: 54544
Rectangular floors having perimeter of 16 meters are to be covered wit  [#permalink]

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07 Jul 2017, 00:21
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Difficulty:

15% (low)

Question Stats:

79% (01:34) correct 21% (01:46) wrong based on 79 sessions

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Rectangular floors having perimeter of 16 meters are to be covered with carpet squares that measure 1 meter by 1 meter each, costing $6 apiece. What is the maximum possible cost for the number of carpet squares needed to cover any such rectangular floor if the sides of the floors are integers? (A)$42
(B) $72 (C)$90
(D) $96 (E)$120

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Joined: 14 Oct 2015
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Rectangular floors having perimeter of 16 meters are to be covered wit  [#permalink]

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07 Jul 2017, 03:06
3
Bunuel wrote:
Rectangular floors having perimeter of 16 meters are to be covered with carpet squares that measure 1 meter by 1 meter each, costing $6 apiece. What is the maximum possible cost for the number of carpet squares needed to cover any such rectangular floor if the sides of the floors are integers? (A)$42
(B) $72 (C)$90
(D) $96 (E)$120

If perimeter is 16,

L + W = 8

If we have integer sides, we can have these combinations.

2 and 6
3 and 5
4 and 4

Since area is maximum when it is a square i.e. 16,

We have $$16 * 6 = 96$$
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Re: Rectangular floors having perimeter of 16 meters are to be covered wit  [#permalink]

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07 Jul 2017, 04:24
You do not have to try any combination of numbers to figure out the maximum. This is because with a 4 sided figure, for any given perimeter, a square maximized the area.

Thus 2x + 4y = 16 becomes 4s = 16;
Each side is 4 so the maximum area is 16;
16*$6 =$96;
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Re: Rectangular floors having perimeter of 16 meters are to be covered wit  [#permalink]

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12 Jul 2017, 16:34
1
Bunuel wrote:
Rectangular floors having perimeter of 16 meters are to be covered with carpet squares that measure 1 meter by 1 meter each, costing $6 apiece. What is the maximum possible cost for the number of carpet squares needed to cover any such rectangular floor if the sides of the floors are integers? (A)$42
(B) $72 (C)$90
(D) $96 (E)$120

Since we want the maximum possible cost of the carpet, we want the maximum possible area of a rectangle whose perimeter is 16 meters. The maximum possible area of a rectangle with a given perimeter is a square. Thus, if we let s = side of the square, then 4s = 16 or s = 4 meters. Thus, the area of the square is s^2 = 4^2 = 16 square meters. Since each carpet squares is 1 square meter and costs $6, we need 16 carpet squares totalling 16 x$6 = \$96.

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Re: Rectangular floors having perimeter of 16 meters are to be covered wit   [#permalink] 12 Jul 2017, 16:34
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