Graduate Management Admission Test (GMAT) Practice Test

Which of the following is a known right triangle with integer dimensions?

1. 3:5:7

2. 3:4:5

3. 8:10:12

4. 6:8:10

The correct answer is: 3:4:5

A right triangle is defined by the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse. In the case of the triangle with dimensions 3, 4, and 5: - The lengths are \( 3 \), \( 4 \), and \( 5 \). - To check if this is a right triangle, we calculate: \[ 3^2 + 4^2 = 9 + 16 = 25 \] \[ 5^2 = 25 \] Since both sums are equal, it confirms that the triangle with the dimensions 3, 4, and 5 is indeed a right triangle. The triangle with dimensions 3, 5, and 7 does not satisfy the Pythagorean theorem, as: \[ 3^2 + 5^2 = 9 + 25 = 34 \neq