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# What is the perimeter of right triangle XYZ?

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What is the perimeter of right triangle XYZ? [#permalink]

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24 Jan 2013, 17:22
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What is the perimeter of right triangle XYZ?

(1) XY = 11
(2) XZ = 11

Question # 123 from Total GMAT Math:

So far I've deduced that Y and Z are equal, making them the legs of a 45 -45 - 90 triangle. I've yet to figure out how to manipulate the equations to come up with leg length of 11 and hypotenuse of 11 rt(2). Please help, sorry if its a repost. Searched and couldn't find anything.
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Jan 2013, 05:18, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Right Triangles Question # 123 -- Total GMAT Math [#permalink]

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24 Jan 2013, 18:22
ereyhan wrote:
Question # 123 from Total GMAT Math:

What is the perimeter of right triangle XYZ?

1. XY = 11
2. XZ = 11

So far I've deduced that Y and Z are equal, making them the legs of a 45 -45 - 90 triangle. I've yet to figure out how to manipulate the equations to come up with leg length of 11 and hypotenuse of 11 rt(2). Please help, sorry if its a repost. Searched and couldn't find anything.

It is a data sufficiency problem, so you don't have to solve. You only have to know what you need in order to solve. So far it sounds like you have realized that you need both statements in order to deduce that x is the 90 degree corner. You know you have the length of the two legs, so you know you can solve the hypotenuse; so you can solve perimeter.

If you were trying to solve for the actual value of the hypotenuse, use the pythagorean theorem. $$a^2 +b^2 = c^2$$

$$11^2 + 11^2 = c^2$$
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Re: Right Triangles Question # 123 -- Total GMAT Math [#permalink]

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24 Jan 2013, 20:28
ereyhan wrote:
Question # 123 from Total GMAT Math:

What is the perimeter of right triangle XYZ?

1. XY = 11
2. XZ = 11

So far I've deduced that Y and Z are equal, making them the legs of a 45 -45 - 90 triangle. I've yet to figure out how to manipulate the equations to come up with leg length of 11 and hypotenuse of 11 rt(2). Please help, sorry if its a repost. Searched and couldn't find anything.

A couple of things about a right triangle:

- The hypotenuse is the longest side. No other side can be equal to or longer than the hypotenuse.
- The relation between the sides and the hypotenuse of the triangle is given by side^2 + side^2 = hypotenuse^2

Given the right triangle XYZ, we cannot say whether the hypotenuse is XY, YZ or XZ.

1. XY = 11
2. XZ = 11

We know the length of two sides. Since the lengths are equal, we can be sure that neither one of them is the hypotenuse. The hypotenuse must be YZ. So get the perimeter, we need to know all three sides so we need to know the hypotenuse too.

$$11^2 + 11^2 = YZ^2$$
$$2*11^2 = YZ^2$$
$$YZ = 11\sqrt{2}$$

Perimeter = $$11 + 11 + 11\sqrt{2}$$

I would advice you to check out a geometry book (Take a look at the Veritas Geometry book here: http://www.amazon.com/Geometry-Veritas- ... s+geometry ) for all these concepts.
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Re: Right Triangles Question # 123 -- Total GMAT Math [#permalink]

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29 Jan 2013, 07:32
Hi,
Since we know that it's a 45-45-90 triangle (combining 1 and 2),we know that the length of the hypotenuse would be xroot2..where x is 11...So answer should be C..Am I right ?

VeritasPrepKarishma wrote:
ereyhan wrote:
Question # 123 from Total GMAT Math:

What is the perimeter of right triangle XYZ?

1. XY = 11
2. XZ = 11

So far I've deduced that Y and Z are equal, making them the legs of a 45 -45 - 90 triangle. I've yet to figure out how to manipulate the equations to come up with leg length of 11 and hypotenuse of 11 rt(2). Please help, sorry if its a repost. Searched and couldn't find anything.

A couple of things about a right triangle:

- The hypotenuse is the longest side. No other side can be equal to or longer than the hypotenuse.
- The relation between the sides and the hypotenuse of the triangle is given by side^2 + side^2 = hypotenuse^2

Given the right triangle XYZ, we cannot say whether the hypotenuse is XY, YZ or XZ.

1. XY = 11
2. XZ = 11

We know the length of two sides. Since the lengths are equal, we can be sure that neither one of them is the hypotenuse. The hypotenuse must be YZ. So get the perimeter, we need to know all three sides so we need to know the hypotenuse too.

$$11^2 + 11^2 = YZ^2$$
$$2*11^2 = YZ^2$$
$$YZ = 11\sqrt{2}$$

Perimeter = $$11 + 11 + 11\sqrt{2}$$

I would advice you to check out a geometry book (Take a look at the Veritas Geometry book here: http://www.amazon.com/Geometry-Veritas- ... s+geometry ) for all these concepts.
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Re: Right Triangles Question # 123 -- Total GMAT Math [#permalink]

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20 Feb 2013, 16:20

farukqmul wrote:
Hi,
Since we know that it's a 45-45-90 triangle (combining 1 and 2),we know that the length of the hypotenuse would be xroot2..where x is 11...So answer should be C..Am I right ?

VeritasPrepKarishma wrote:
ereyhan wrote:
Question # 123 from Total GMAT Math:

What is the perimeter of right triangle XYZ?

1. XY = 11
2. XZ = 11

So far I've deduced that Y and Z are equal, making them the legs of a 45 -45 - 90 triangle. I've yet to figure out how to manipulate the equations to come up with leg length of 11 and hypotenuse of 11 rt(2). Please help, sorry if its a repost. Searched and couldn't find anything.

A couple of things about a right triangle:

- The hypotenuse is the longest side. No other side can be equal to or longer than the hypotenuse.
- The relation between the sides and the hypotenuse of the triangle is given by side^2 + side^2 = hypotenuse^2

Given the right triangle XYZ, we cannot say whether the hypotenuse is XY, YZ or XZ.

1. XY = 11
2. XZ = 11

We know the length of two sides. Since the lengths are equal, we can be sure that neither one of them is the hypotenuse. The hypotenuse must be YZ. So get the perimeter, we need to know all three sides so we need to know the hypotenuse too.

$$11^2 + 11^2 = YZ^2$$
$$2*11^2 = YZ^2$$
$$YZ = 11\sqrt{2}$$

Perimeter = $$11 + 11 + 11\sqrt{2}$$

I would advice you to check out a geometry book (Take a look at the Veritas Geometry book here: http://www.amazon.com/Geometry-Veritas- ... s+geometry ) for all these concepts.
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Re: What is the perimeter of right triangle XYZ? [#permalink]

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24 Oct 2015, 10:16
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Re: What is the perimeter of right triangle XYZ?   [#permalink] 24 Oct 2015, 10:16
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