Hello,

I was wondering if anyone can help me in answering this question.
If a rectangle is cut diagionally ... does it form two 30, 60, 90 right triangles?

Thanks All!

Not possible, assuming 90 is the length of the diagonal, the other 2 sides cannot be 30,60, since square root of ( 30^2 + 60^2) is not 90.

Are you sure you are not missing any details in the question?

I'm not sure if I explained my question fully.take a rectangle and cut it diagionally. Are the two new triangles formed here take the form of a 30 60 90 degree right triangle. With this being said can we calculate the peremiter given the hypotonuse is 4 ....then the perimeter of the rectangle would be 2 + 2 + 2 rd 3 +2 rd 3

If a rectangle is cut diagonally, the two traingles formed may or may not be 30 60 90 triangle. It depends on the length of the sides of rectangle. If the ratio of length to breadth of the rectangle is (sqrt 3):1 then only it will form 30 60 90 triangle.

That was great!!! Thanks a lot!!

Nice job smohit. Yes, those proportions will tell us that we are dealing with a 30-60-90 triangle because of the 30-60-90 triangle rule.

_________________
Jamie Nelson
ManhattanGMAT Instructor

Jamie or Mohit,

How does the length determine? I understand that a rectangle can be divided into 30-60-90 OR 45-45-90, but how does the length help?

Please explain.

Thanks,
Sahana

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Thanks,
Sahana
Never say Never!

Sahana,
Do you have a good math review book? If you do, you will find that 45-45-90 and 30-60-90 triangles have very specific rules associated with them. Specifically:

1) A 45-45-90 triangle has one right angle (which opens to the longest side, or the hypoteneuse) and two equal legs. The lengths of these three sides are expressed as x, x, and xsqrt2, with x across from the 45 degree angles and xsqrt2 across from the 90 degree angle. So for example, we could have 5, 5, 5sqrt2 as the lengths of this triangle.

2) A 30-60-90 triangle's side proportions are different:
a) The 30 degree angle opens to a side we can consider x.
b) The 60 degree angle opens to a side that is xsqrt3.
c) The 90 degree angle opens to a side that is 2x.
For example, this triangle could have lengths 4, 4sqrt3, 8.

This sort of review is really beyond the scope of this forum, so I recommend you either consult our Geometry strategy guide or any good basic geometry book to learn more about these types of special right triangles. They are very important to know for the GMAT.

_________________
Jamie Nelson
ManhattanGMAT Instructor

is there a list of properties of quad, squares, rec, rhombus, etc:

is a rhombus if:


is a square if:

munny, you may wish to consult the ManhattanGMAT Geometry strategy guide which will contain lots of good information in this area.

_________________
Jamie Nelson
ManhattanGMAT Instructor

Have all the books- was just hoping for summary especially as it pertains to Data Sufficiency ie what is minimum info (angles, sides lengths, parrellism, diagonals, etc.) necessary to conclude something is a rhombus, square, etc. ; what implies what and why

Hmm . . . unfortunately I'm not aware of such a resource. May I suggest that you consider compiling your own? I've found that the process of writing information down helps me process and remember it much better than if I just read it. Otherwise, if you google you may also find resources on the web. Good luck!

_________________
Jamie Nelson
ManhattanGMAT Instructor