We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Here is this week’s problem:

In the diagram above, triangle

ABCis equilateral, figureSQREis a square, andAis the midpoint ofSQ. If the perimeter of triangleABCis 6 inches, what is the length, in inches, of segmentRY?

To see the answer choices, and to submit your answer, visit our Challenge Problem Showdown page on our site.

Discuss this week’s problem with like-minded GMAT takers on our Facebook page.

The weekly winner, drawn from among all the correct submissions, will receive One Year of Access to our Challenge Problem Archive, AND the GMAT Navigator, AND Our Six Computer Adaptive Tests ($92 value).

First, QR equals to height of triangle. Because ABC equilateral, side of triangle = 2 (6/3=2). Height of triangle we could find using formulae of equilateral triangle or as the side of right triangle with hypotenuse = 2, other side =1 (2/2=2). Using Pythagorean theorem:

2^2=1^2+x^2

x=square root of 3 = approx. 1,73 is the Height of ABC = SQ = SE = ER = QR

Find RB. 1 (half of the CB) – 1,73/2 (SQ/2) = 0,135

Using Right triangle Sine, Cos, Tan formulae, providing that angle B = 60 degrees, so angle Y = 30 degrees, find RY:

RY = 0,135*1,73 (square root of 3, Tangent of 30 degrees) = approx 0,23

Sorry for my English, I`m first time writing math in English.

And I think, it will be great, if you could include function of attaching pictures

Sorry there is an error Tangent of 60 degree, not 30

thank you Doniyor for your answer, but as you in GMAT we don’t have calculators, how are we supposed to find out what is the tangent of 30 degrees by manual calculation?

Would appreciate your prompt reply

thank you Doniyor for your answer, but as you in GMAT we don’t have calculators, how are we supposed to find out what is the tangent of 30 degrees by manual calculation?

Would appreciate your prompt reply

1.Since the perimeter of triangle is 6 inches,So AB=AC=CB=2 inches.

2.And the triangle is equilateral triangle each angle will be 60.

3.Height of triangle can be find using formulae of equilateral triangle or as the side of right triangle with hypotenuse = 2, other side =1 (2/2=2). Using Pythagorean theorem:

2^2=1^2+x^2

x=square root of 3 = approx. 1,73 is the Height of ABC = SQ = SE = ER = QR

4.CE=RB=(2-1.73)/2=0.27/2

5.Consider the RYB

angle RBY=60Because its a equilateral triangle

Tan60=RY/RB

=>RY=RBTan60

0.27*1.732/2

=0.23

6.Hence RY=0.23

Hello, my response is Sqrt3 – 1.5