Graduate Management Admission Test (GMAT) Practice Test

What are the dimensions of an isosceles right triangle?

1. x:x:x

2. x:x:x√2

3. x:x:2x

4. x:x√3:2x

The correct answer is: x:x:x√2

To understand why the dimensions of an isosceles right triangle are correctly represented by the ratio x:x:x√2, it’s important to consider the properties of these types of triangles. In an isosceles right triangle, two sides are of equal length, and these sides are typically referred to as the legs of the triangle. In this case, let's denote these equal sides as x. According to the Pythagorean theorem, when you have a right triangle, the relationship between the lengths of the legs and the length of the hypotenuse is given by the formula: \( a^2 + b^2 = c^2 \) In an isosceles right triangle, since both legs are equal (let’s say x for both), the formula can be simplified to: \( x^2 + x^2 = c^2 \) This means: \( 2x^2 = c^2 \) By taking the square root of both sides to find the length of the hypotenuse (c), we have: \( c = \sqrt{2x^2} = x\sqrt{2} \) Thus, the dimensions of an isosceles right triangle can be expressed as x