Register for an Upcoming Free GRE Webinar

# 2. The area of an isosceles...

PowerScore StaffJoined: 10/31/2016

# Description

• Type: Quantitative Comparison
• Topic: Geometry
• Special Triangles
• Draw a Figure
• Answer: A, Quantity A is greater

# Explanation

Consider scratch work above.
1. Start by Recording What You Know™, drawing figures, and getting your Possibility Matrix™ and answer choices set up.
2. Write any equations you will need, in this case the area of a triangle equation.
3. An isosceles right triangle with two sides equal to 2 will have 2 as both the base and height.
4. Thus, we can calculate the value of column A (in blue): 2
5. An equilateral right triangle with sides equal to 2 will have a base of 2, but we have to determine the height.
6. Drop a line down from the vertex of the top angle.
7. This line bisects the base and forms a 30:60:90 special right triangle.
8. Note the ratios of the sides of a 30:60:90 right triangle (in green).
9. Use the values of this equilateral triangle to determine the height. a = 1, a­­√3 = √3
10. The height of the equilateral triangle (in red) is √3.
11. Thus, the area of this triangle is √3.
12. √3 ≈ 1.7
13. Column A is greater.
Tagged:
Tagged: