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Here is this week’s problem:

In the diagram above, triangle ABC is equilateral, figure SQRE is a square, and A is the midpoint of SQ. If the perimeter of triangle ABC is 6 inches, what is the length, in inches, of segment RY ?

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### 6 responses to GMAT Challenge Problem Showdown: November 11, 2013

1. 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

2. 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?

3. 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?

4. 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

5. Hello, my response is Sqrt3 – 1.5