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## Official Guide Explanation:

Problem Solving #71

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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**Solution and Metadata**

**Question****: 71**

Page: 71

Difficulty: **5** (Moderate)

Category 1: Geometry > Triangles > Multiple figures

Category 2: Geometry > Triangles > Special Tris

Category 3: Geometry > Triangles > Pythag

**Explanation:** To find the area of BCD, we need the base and the height--two dimensions of the triangle that are perpendicular. Since BCD is a right triangle, those are two sides: BC and BD. We're given BC = 4, so we need BD.

BD is the hypotenuse of BAD, and we know the two other sides of BAD. Since the two legs are equal, it is a 45:45:90 triangle, meaning that the hypotenuse is rt[2] times greater than the length of each leg. Thus, BD = 4 rt[2].

Now we can solve for area: (1/2)bh = (1/2)(4 rt[2])(4) = 8 rt[2], choice (C).

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