Graduate Management Admission Test (GMAT) Practice Test

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In a 30-60 right triangle, which ratio describes its sides?

x:2x:x√3
x:x√2:2x
x:x:x√3
x:x√3:2x

The correct answer is: x:x√3:2x

In a 30-60 right triangle, the angles are 30 degrees, 60 degrees, and 90 degrees. The sides opposite these angles have specific ratios that are derived from the properties of special triangles. For a 30-60-90 triangle, the side lengths can be expressed in terms of a common variable. The ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles respectively is 1 : √3 : 2. This means that if we let the length of the side opposite the 30° angle be x, then the side opposite the 60° angle will be x√3, and the hypotenuse (opposite the 90° angle) will be 2x. In the provided ratios, the correct one matches this established ratio. The variable x represents the length of the side opposite the 30-degree angle, x√3 represents the length of the side opposite the 60-degree angle, and 2x represents the hypotenuse. Therefore, the ratio that describes the sides of a 30-60 right triangle is x : x√3 : 2x, affirming that the choice is accurate according to the properties of