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# 45-45-90 triangles and their side ratio

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Joined: 07 Aug 2017
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45-45-90 triangles and their side ratio  [#permalink]

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19 Aug 2017, 03:20
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Difficulty:

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Question Stats:

100% (04:44) correct 0% (00:00) wrong based on 3 sessions

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Below PS question is from the official guide.

Attachment:

Figure X and Y.JPG [ 11.3 KiB | Viewed 465 times ]

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

(A) 2:3
(B) \sqrt{2} :2
(C) 2 \sqrt{2}:3
(D) 1:1
(E) \sqrt{2}:1

Figures X and Y are attached to this post.
Answer given in official guide - C

Now figure X is a square and it can be derived that the two triangles are isosceles triangles which gives us a 45-45-90 triangle. Now the sides of this triangle should be in the ratio 1:1:\sqrt{2}. So sides of triangle can be a:a:a \sqrt{2}. Where the hypotenuse is a \sqrt{2}. However the explanation in OG considers two legs of triangle as a \sqrt{2}.

Can someone please explain me where I am going wrong?

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Re: 45-45-90 triangles and their side ratio  [#permalink]

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19 Aug 2017, 03:25
1
GMATMBA5 wrote:
Below PS question is from the official guide.

Attachment:
Figure X and Y.JPG

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

(A) 2:3
(B) \sqrt{2} :2
(C) 2 \sqrt{2}:3
(D) 1:1
(E) \sqrt{2}:1

Figures X and Y are attached to this post.
Answer given in official guide - C

Now figure X is a square and it can be derived that the two triangles are isosceles triangles which gives us a 45-45-90 triangle. Now the sides of this triangle should be in the ratio 1:1:\sqrt{2}. So sides of triangle can be a:a:a \sqrt{2}. Where the hypotenuse is a \sqrt{2}. However the explanation in OG considers two legs of triangle as a \sqrt{2}.

Can someone please explain me where I am going wrong?

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Re: 45-45-90 triangles and their side ratio  [#permalink]

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19 Aug 2017, 11:32
GMATMBA5 wrote:
Below PS question is from the official guide.

Attachment:
Figure X and Y.JPG

Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?

(A) 2:3
(B) \sqrt{2} :2
(C) 2 \sqrt{2}:3
(D) 1:1
(E) \sqrt{2}:1

Figures X and Y are attached to this post.
Answer given in official guide - C

Now figure X is a square and it can be derived that the two triangles are isosceles triangles which gives us a 45-45-90 triangle. Now the sides of this triangle should be in the ratio 1:1:\sqrt{2}. So sides of triangle can be a:a:a \sqrt{2}. Where the hypotenuse is a \sqrt{2}. However the explanation in OG considers two legs of triangle as a \sqrt{2}.

Can someone please explain me where I am going wrong?

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: 45-45-90 triangles and their side ratio   [#permalink] 19 Aug 2017, 11:32
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