Graduate Management Admission Test (GMAT) Practice Test

Which triangle is specifically defined as having sides in the ratio 8:15:17?

1. Scalene triangle

2. Isosceles triangle

3. Equilateral triangle

4. Right triangle

The correct answer is: Right triangle

The triangle with sides in the ratio of 8:15:17 is defined as a right triangle. This is determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, if we let the sides be 8, 15, and 17, we can check if they satisfy the theorem: - The hypotenuse would be 17, and the other two sides are 8 and 15. Calculating the squares: - \(8^2 = 64\) - \(15^2 = 225\) - \(17^2 = 289\) Now, adding the squares of the two shorter sides: - \(64 + 225 = 289\) Since \(289 = 289\), this confirms that the triangle described by the sides in the ratio 8:15:17 indeed forms a right triangle. This specific ratio corresponds to the lengths of a common Pythagorean triple, making it clear that not only does it satisfy the triangle inequality, but it also fits