Official Guide Explanation:
Data Sufficiency #D48




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Solution and Metadata

Question: D48
Page: 25
Difficulty: 5 (Moderate)
Category 1: Geometry > Quadrilaterals >
Category 2: Geometry > Triangles > Pythag

Explanation: We're looking for the perimeter of a rectangle. To find that, we'll need both the length and width.

Statement (1) is insufficient. The diagonal is the same as the hypotenuse of a right triangle formed with the length and width as legs. Using the pythagorean theorem:

l2 + w2 = 102

Two variables and one equation isn't enough.

Statement (2) is also insufficient. This tells us that lw = 48. Again, it's two variables and one equation. The side lengths could be 12 and 4, 6 and 8, or any number of other possibilities.

Taken together, the statements are sufficient. Given two equations with two variables, we can solve. To do so algebraically would be unnecessary and too arduous for the time constraints of a DS question. However, if you recall common triangle ratios, if the hypotenuse is 10, the sides could be 6 and 8. Since that gives you an area of 48, 6 and 8 are the length and width, resulting in a perimeter of 28. Choice (C) is correct.

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