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The width and the length of a rectangular piece of plywood

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Carcass
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The width and the length of a rectangular piece of plywood [#permalink] New post   09 Dec 2017, 16:11
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The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip x inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed. For what value of x will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)

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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   15 Dec 2017, 09:08
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If I understood right, we removed x wide around the rectangular piece of plywood to get a new ratio 2/5
So the actual ration is 4/8 and since we removed to each of the lenght x we can write as follows
(4-x)/(8-x) = 2/5
We cross multiply
2(8-x) = 5(4-x)
16× - 2x = 20-5x
Which gives us at the end x = 4/3
Since 1 foot is 12 inches, we multiply 4/3 by 12 and we get the 16...
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   15 Dec 2017, 08:22
Not getting the correct answer but I may not be understanding the solution correctly. Anyone have a worked answer for this one?
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   29 Apr 2019, 08:02
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along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed.
why it doesn't mean that along 4-foot edge, a strip x inches wide is removed?
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   01 May 2019, 11:39
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Not sure I get what did you mean.

Could you please elaborate better ??

Thank you
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   16 Oct 2019, 12:47
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Carcass wrote:
The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip x inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed. For what value of x will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)

enter your value

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"Along one edge of the plywood, a strip x inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed."

this would mean that there are two strips one which is 8(x) and one that is 4(x). The strip shares a square area that is x^2 big. Therefore the area of the strips would be 8(x)+ 4(x)-x^2. I am unsure how you would derive the value of x that would give a ratio of 2:5
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   17 Oct 2019, 13:54
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SusieSushi wrote:
Carcass wrote:
The width and the length of a rectangular piece of plywood are 4 feet and 8 feet, respectively. Along one edge of the plywood, a strip x inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed. For what value of x will the remaining rectangular piece have width and length in the ratio of 2 to 5? (1 foot = 12 inches)

enter your value

Show: :: OA
16


"Along one edge of the plywood, a strip x inches wide and 8 feet long is removed. Then, along an edge perpendicular to the 8-foot edge, a strip x inches wide is removed."

this would mean that there are two strips one which is 8(x) and one that is 4(x). The strip shares a square area that is x^2 big. Therefore the area of the strips would be 8(x)+ 4(x)-x^2. I am unsure how you would derive the value of x that would give a ratio of 2:5



You are probably missing the idea here that the second strip is removed after first is removed. Resulting rectangle after removing 1st srip has dimension (length = 8 and width = 4-x).This is the rectangle from which the second strip gets removed resulting the final rectangle with length = 8-x and width = 4-x.
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Re: The width and the length of a rectangular piece of plywood [#permalink] New post   06 Oct 2024, 21:24
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let's transform all the values to inches width = 48 length =96 after removing x inches and 8 foot strip along the edge remaining width will be (48-x)inches now we remove another strip perpendicular to the previous one now the length becomes (96-x) so as to make the new ratio 2/5 we do the following calculation (48-x)/(96-x) = 2/5 after doing this calculation we'll have x = 16
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Re: The width and the length of a rectangular piece of plywood [#permalink]
06 Oct 2024, 21:24
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