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Math Expert V
Joined: 02 Sep 2009
Posts: 56256
Re: What is the area of rectangular region R ?  [#permalink]

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mrdlee23 wrote:
Can someone please explain why we can't make four triangles out of the rectangle to determine the third side of each triangle?

How would you do that? Knowing the lengths of the two sides of a triangle is not enough to find the length of the third side.

P.S. This post might also help: https://gmatclub.com/forum/what-is-the- ... ml#p824049
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Intern  S
Joined: 29 Jan 2017
Posts: 44
Re: What is the area of rectangular region R ?  [#permalink]

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I am fairly weak in quant (especially geometry and number properties); I didn't know that the pythagorean theorem applies only to right triangles.

Thanks

Bunuel wrote:
mrdlee23 wrote:
Can someone please explain why we can't make four triangles out of the rectangle to determine the third side of each triangle?

How would you do that? Knowing the lengths of the two sides of a triangle is not enough to find the length of the third side.

P.S. This post might also help: https://gmatclub.com/forum/what-is-the- ... ml#p824049
Math Expert V
Joined: 02 Sep 2009
Posts: 56256
Re: What is the area of rectangular region R ?  [#permalink]

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mrdlee23 wrote:
I am fairly weak in quant (especially geometry and number properties); I didn't know that the pythagorean theorem applies only to right triangles.

Thanks

Bunuel wrote:
mrdlee23 wrote:
Can someone please explain why we can't make four triangles out of the rectangle to determine the third side of each triangle?

How would you do that? Knowing the lengths of the two sides of a triangle is not enough to find the length of the third side.

P.S. This post might also help: https://gmatclub.com/forum/what-is-the- ... ml#p824049

I suggest to read the following topics:
ALL YOU NEED FOR QUANT ! ! !

For Geometry check below:

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Re: What is the area of rectangular region R ?  [#permalink]

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This one doesn't make sense to me. It says that both diagonals are of equal length. That is only possible if the rectangular is a square (a special form of a rectangle). If each diagonal is 5, then each side of the square can be calculated as root of (2.5^2+2.5^2). If each side can be determined, it is sufficient (A).

What am I missing.
Math Expert V
Joined: 02 Sep 2009
Posts: 56256
Re: What is the area of rectangular region R ?  [#permalink]

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gmattaker111 wrote:
This one doesn't make sense to me. It says that both diagonals are of equal length. That is only possible if the rectangular is a square (a special form of a rectangle). If each diagonal is 5, then each side of the square can be calculated as root of (2.5^2+2.5^2). If each side can be determined, it is sufficient (A).

What am I missing.

1. All rectangles, not necessarily square, have equal diagonals.
2. If the diagonal of a square is 5, then x^2 + x^2 = 5^2, not what you've written.
3. You should brush-up fundamentals. Check the the links here: https://gmatclub.com/forum/what-is-the- ... l#p1903104

Hope it helps.
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Re: What is the area of rectangular region R ?  [#permalink]

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Statement 1: By only from diagonal we cannot tell the area of Rectangle. Insufficient
Statement: B y only from perimeter we cannot tell the area of the Rectangle . Insufficient.

Both A & B we can tell the area of Rectangle So sufficient.
C
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Re: What is the area of rectangular region R ?  [#permalink]

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So, just to check: If the stem said that it was a SQUARE RECTANGLE, then (1) would be Sufficient.

¿Am I right?

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the area of rectangular region R ?  [#permalink]

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ajit257 wrote:
What is the area of rectangular region R ?

(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

A rectangular has 2 variables.

Since we have 2 variables and 0 equations, C is most likely to be the answer and so we should consider 1) & 2) first.

Conditions 1) & 2)

We have a^2 + b^2 = 5^2 = 25 from the condition 1).
We have 2(a+b) = 14 or a+b=7 from the condition 2).

2ab = (a+b)^2 - (a^2+b^2) = 7^2 - 25 = 49 - 25 = 24
Thus the area of the rectanglular ab is 12.

Regarding VA method for geometry, we can count the number of variables for geometry questions as follows.
A circle has 1 variable.
A triangle has 3 variables.
A square has 1 variable.
A rectangle has 2 variables.
A rhombus has 2 variables.
A parallelogram has 3 variables.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: What is the area of rectangular region R ?  [#permalink]

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ajit257 wrote:
What is the area of rectangular region R ?

(1) Each diagonal of R has length 5.
(2) The perimeter of R is 14.

diagonal^2 = $$l^2 + b^2$$

From 1, Cannot say anything about l & b
25 = $$l^2 + b^2$$

From 2, 2(l+b) = 14

l + b = 7

Cannot say anything about l & b

Combine, $${l+b}^2 = 49$$

Just open the square and put back the values to get an unique answer.
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Manager  S
Joined: 26 Sep 2018
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Location: Sweden
Re: What is the area of rectangular region R ?  [#permalink]

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Nowhere in the question is it mentioned that the sides are integers.
Thanks.
Intern  B
Joined: 29 Jul 2018
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Re: What is the area of rectangular region R ?  [#permalink]

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Rectangle has 90 degrees each, so if I draw diagonal then there will be 2 triangles 0f 45-45-90. If diagonal is 5 then I will be able to figure out other sides too.. isn’t A sufficient? Where am I going wrong? Please help.

Posted from my mobile device Re: What is the area of rectangular region R ?   [#permalink] 18 Jul 2019, 02:00

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