In Isosceles Triangle EFG Above, Angle FEG Measures 60 Degrees GMAT Problem Solving

Question:

In isosceles triangle EFG above, angle FEG measures 60 degrees and side FG measures 10 centimeters. What is the length in centimeters, of side EG?

1. 10
2. 15
3. 20
4. 30
5. Cannot be determined

“In isosceles triangle EFG above, angle FEG measures 60 degrees “ - is a topic that is covered in the quantitative reasoning section of the GMAT. To successfully execute the GMAT Problem Solving questions, a student must possess a wide range of qualitative skills. The entire GMAT Quant section consists of 31 questions. The problem-solving section of the GMAT Quant topics requires the solution of calculative mathematical problems.

Solutions and Explanation

Approach Solution : 1

Triangle EFG is an equilateral triangle, no matter how it is looked into

Instance 1: If angle FEG = angle FGE (an isosceles triangle property) = 60 degrees, angle EFG will also be 60 degrees.

Instance 2: If angle FEG = angle EFG (an isosceles triangle property) = 60 degrees, angle FGE will also be 60 degrees.

Instance 3: If angle EFG = angle FGE (an isosceles triangle property) = (180-60)/2 = 60 degrees.

Triangle EFG is an equilateral triangle since it will always have three angles that are all 60 degrees in all instances.

As a result, if one side is 10 cm, all of the sides will also be 10 cm. Thus, side EG = 10 cm.

Correct Answer: (A)

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