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Re: If a rectangular region has perimeter P inches and area A sq
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21 Sep 2013, 06:29
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olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square? 1) P=4/3A 2)P=4√A
Lets try finding the relation between area and perimeter of a square. We know the area of a square with length x (A) = x^2 The perimeter of the square (P) = 4x
Since P = 4x --> x = P/4
So, A = (P/4)^2 A =(P^2)/16 Therefore, P^2 = 16A and P = 4*sqrtA
Re: If a rectangular region has perimeter P inches and area A sq
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21 Sep 2013, 06:40
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olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square? 1) P=4/3A 2)P=4√A
for a rectangle Perimeter P=2(l+b) Area A=l*b
From 1) 2(l+b)=4/3*(l*b) 6(l+b)=4(l*b) 3(l+b)=2(l*b) this equation satisfies for l=3 and b=3, dimensions of a square and at l=6,b=2 dimensions of a rectangle..hence not sufficient
From 2) 2(l+b)=4√(l*b) (l+b)=2√(l*b) squaring both sides (l+b)^2=4l*b (l-b)^2=0 l=b,which is a square, Sufficient
Re: If a rectangular region has perimeter P inches and area A sq
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16 Dec 2014, 12:56
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olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
(1) P = 4/3*A (2) P = 4√A
I would solve this question by simply plugging in numbers.
1. Let's assume the rectangular is indeed a square. 2. Let's assume the side of the square is 4.
If the side of this square is 4: The perimeter would be 16 and the area would be 16 as well.
(S1) P = 4/3√A If the rectangular is a square, all values for A area should correspond with the right value for P. In my assumed case: if the perimeter is 16 , the area should be 16 too. In this case : 16 is not equal to 4/3*16 , so we can't say for sure that this rectangle indeed is a square.
(S2) P = 4√A 16=4*√16 We got a match!
If you want to be sure , try any other plugin for a square. Lets say the side of the rectangle is 2. For it to be a square the perimeter should be 8(2+2+2+2) and the area is 4(2*2) 8=4√4 So as you can see , S2 will hold true for any plugin.A _________________
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Re: If a rectangular region has perimeter P inches and area A sq
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30 Mar 2015, 11:01
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kusena wrote:
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square? 1) P=4/3A 2)P=4√A
for a rectangle Perimeter P=2(l+b) Area A=l*b
From 1) 2(l+b)=4/3*(l*b) 6(l+b)=4(l*b) 3(l+b)=2(l*b) this equation satisfies for l=3 and b=3, dimensions of a square and at l=6,b=2 dimensions of a rectangle..hence not sufficient
From 2) 2(l+b)=4√(l*b) (l+b)=2√(l*b) squaring both sides (l+b)^2=4l*b (l-b)^2=0 l=b,which is a square,Sufficient
This can be Rhombus as well right?Even Rhombus has all sides equal. So how can we confidently say that it is a square. We dont know whether the diagonals are equal
Would really appreciate if someone can clear my doubt
Re: If a rectangular region has perimeter P inches and area A sq
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30 Mar 2015, 17:36
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Expert Reply
Hi buddyisraelgmat,
The prompt refers to a RECTANGULAR REGION, so the four corners must be 90 degrees each. Thus, we're dealing with either a rectangle of some kind or a square.
Re: If a rectangular region has perimeter P inches and area A sq
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19 Oct 2015, 10:58
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olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
(1) P = 4/3*A (2) P = 4√A
I would also solve by plugging in values:
Let's create two rectangular regions which are squares:
Generally: P = 4s (where s is the side of a square) and \(A = s^2\)
First square with side 2: P = 8 and A = 4
Second square with side 3: P = 12 and A = 9
Statement 1: Gives you a yes on the square with side 3 because P = 4/3 * A but a no for the square with side 2. Statement 2: \(P = 4*\sqrt{A}\) - this is true for both squares we created. Fair enough, Answer B.
Re: If a rectangular region has perimeter P inches and area A sq
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Updated on: 28 Mar 2021, 12:08
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Top Contributor
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
(1) P = (4/3)(A) (2) P = 4√A
Given: A rectangular region has perimeter P inches and area A square inches
Target question:Is the region square? This is a good candidate for rephrasing the target question.
So, what kind of relationship between P and A do we need in order for the rectangular region to be a SQUARE? Well, if the region is a square, then all 4 sides will be the same length So, if P = the perimeter (sum of all 4 sides), then P/4 = the length of each side If P/4 = the length of each side, then the AREA = (P/4)(P/4) In other words: A = (P/4)(P/4) Simplify: A = P²/16 Multiply both sides by 16 to get: 16A = P² Take square root of both sides to get: 4√A = P So, if 4√A = P, then we can be certain that the region is a square. REPHRASED target question:Does 4√A = P?
Below, you'll find a video with tips on rephrasing the target question
Statement 1: P = (4/3)(A) Let's TEST some values. There are several values of P and A that satisfy statement 1. Here are two: Case a: P = 12 and A = 9. In this case, the answer to the REPHRASED target question is YES, 4√A DOES EQUAL P Case b: P = 4 and A = 3. In this case, the answer to the REPHRASED target question is NO, 4√A does NOT equal P Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: P = 4√A Perfect!! The answer to the REPHRASED target question is YES, 4√A DOES EQUAL P Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Re: If a rectangular region has perimeter P inches and area A sq
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21 Jun 2020, 19:32
Expert Reply
waihoe520 wrote:
as a non-english native speaker.
I dont understand what the question is asking.
If a rectangular region has perimeter P inches and area A square inches, is the region square?
My interpretation : a rectangular region, since the the prompt already specified it's a rectangular, why the question is asking if that is a square?
Hi waihoe520,
By definition, a 'rectangular region' has four 90-degree angles and two 'pairs' of opposite sides that are equal in length. Thus, a square IS a rectangle (since a square fits that definition), but most rectangles are NOT squares (since a square has 4 equal sides and most rectangles do not).
Re: If a rectangular region has perimeter P inches and area A sq
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19 Oct 2020, 08:10
Expert Reply
shivali22 wrote:
Hi
abhimahnaBunuel Can you explain why statement 1 is not sufficient ?
As per statement 1
1) P=4/3*A
P= 2(l+b) and A l*b
hence , substituting
2(l+b)=4/3*l*b 6l+6b =4lb 3l+3b=2lb 3l+3b-2lb=0
Rearranging 3l-lb + 3b-lb=0 l(3-b)+b(3-l)=0
-> Since l,b are dimensions of a figure l,b cannot be 0 or negative Therefore to make the above expression 0 l=b=3
Hence statement 1 is sufficient.
2(l+b)=4/3*l*b has infinitely many solutions. Foe example, if l = 10, then b = 30/17. Even if you assume that l and b are integers (which would not be correct), still 2(l+b)=4/3*l*b has more solutions. Foe example, b = 2 and l = 6. _________________
Re: If a rectangular region has perimeter P inches and area A sq
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14 Feb 2021, 17:01
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Hi CEdward,
TESTing VALUES is a great way to approach this question, but you still have to follow all of the 'restrictions' that the prompt gives you (as well as the overall rules of math).
In your example, you have an AREA of 4 and a PERIMETER of 8.
With a 2x2 square, you have an area of 4 and a perimeter of 8, so this is a possible option. With a 1x3 rectangle, you have an area of 3..... but that does NOT match the area of 4 that needs to occur, so a 1x3 rectangle is NOT possible here. The ONLY option that fits this particular combination of area and perimeter is a 2x2 square.
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