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 ?

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.