Question 2 One leg of an isosceles triangle is \( 2 x+5 \) and the other is \( 3 x-2 \). What is the base length? 9.5 7 Cannot be determined 19

To solve the problem, we need to analyze the given information about the isosceles triangle. In an isosceles triangle, two sides are equal in length. 1. **Identify the known conditions:** - One leg of the triangle is \( 2x + 5 \). - The other leg of the triangle is \( 3x - 2 \). Since the triangle is isosceles, we can set the two legs equal to each other: \[ 2x + 5 = 3x - 2 \] 2. **Solve for \( x \):** - Rearranging the equation gives us: \[ 5 + 2 = 3x - 2x \] \[ 7 = x \] 3. **Substituting \( x \) back to find the lengths of the legs:** - For the first leg: \[ 2x + 5 = 2(7) + 5 = 14 + 5 = 19 \] - For the second leg: \[ 3x - 2 = 3(7) - 2 = 21 - 2 = 19 \] Both legs are equal to 19, confirming that the triangle is indeed isosceles. 4. **Determine the base length:** - The problem does not provide any information about the base length of the triangle. Since the base length is not specified or derived from the given information, we cannot determine it. Thus, the answer is: **Cannot be determined**.