**Register for an Upcoming Free GRE Webinar**

Reserve your spot now!

Reserve your spot now!

# 2. The area of an isosceles...

# Description

- Type: Quantitative Comparison
- Topic: Geometry
- Special Triangles
- Draw a Figure

- Answer:
**A, Quantity A is greater**

# Explanation

Consider scratch work above.

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

#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Before you post, please remember:

**Search for your topic**. A discussion may already be waiting for you!

**Focus on one topic per post**. For example, ask about just one practice exercise rather than two or more in a single post.

**Don’t post copyrighted material**. For example, don't post practice exercises from books or courses that must be purchased. Even some free stuff, including from ETS, may be copyrighted and so shouldn't be posted.