\( \triangle C R V \) has side lengths that measure 10 centimeters, 12 centimeters, and 15 centimeters. Which of the following best describes this type of triangle? A. Equilateral triangle B. Isosceles triangle C. Obtuse triangle D. Scalene triangle

To determine the type of triangle \( \triangle CRV \) with side lengths of 10 cm, 12 cm, and 15 cm, we can analyze the properties of the triangle based on its side lengths. 1. **Equilateral Triangle**: All three sides are equal. In this case, the sides are 10 cm, 12 cm, and 15 cm, which are not equal. Therefore, it is not an equilateral triangle. 2. **Isosceles Triangle**: At least two sides are equal. Again, since all three sides are different, it is not an isosceles triangle. 3. **Scalene Triangle**: All three sides are different. Since 10 cm, 12 cm, and 15 cm are all different lengths, this triangle is a scalene triangle. 4. **Obtuse Triangle**: A triangle is obtuse if one of its angles is greater than 90 degrees. To check if this triangle is obtuse, we can use the Pythagorean theorem. We need to see if \( c^2 > a^2 + b^2 \) for the longest side \( c \) (which is 15 cm in this case). - Calculate \( 15^2 \) and \( 10^2 + 12^2 \): \[ 15^2 = 225 \] \[ 10^2 + 12^2 = 100 + 144 = 244 \] Since \( 225 < 244 \), the triangle is not obtuse. Based on this analysis, the best description of triangle \( \triangle CRV \) is: **D. Scalene triangle**.