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45-45-90 triangles and their side ratio

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45-45-90 triangles and their side ratio [#permalink]

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New post 19 Aug 2017, 03:20
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Below PS question is from the official guide.

Attachment:
Figure X and Y.JPG
Figure X and Y.JPG [ 11.3 KiB | Viewed 102 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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Re: 45-45-90 triangles and their side ratio [#permalink]

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New post 19 Aug 2017, 03:25
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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?


Please search before posting a question.

This question is discussed here: https://gmatclub.com/forum/figures-x-an ... 07393.html In case of questions please post in that thread.

Also, please read carefully and follow our RULES OF POSTING. To format formulas properly please check this post: https://gmatclub.com/forum/rules-for-po ... l#p1096628 Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124307 [1], given: 12077

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41660

Kudos [?]: 124307 [0], given: 12077

Re: 45-45-90 triangles and their side ratio [#permalink]

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New post 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?


Also, please read carefully and follow our RULES OF POSTING. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124307 [0], given: 12077

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

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