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 find the base length of the isosceles triangle, we first need to set the two legs equal to each other since they are the same in an isosceles triangle. The legs of the triangle are given as: - Leg 1: \( 2x + 5 \) - Leg 2: \( 3x - 2 \) We can set up the equation: \[ 2x + 5 = 3x - 2 \] Now, let's solve for \( x \) step by step. 1. Subtract \( 2x \) from both sides: \[ 5 = x - 2 \] 2. Add \( 2 \) to both sides: \[ 7 = x \] Now that we have \( x = 7 \), we can substitute this value back into either expression for the legs to find their lengths. Let's calculate the length of the legs: For Leg 1: \[ 2x + 5 = 2(7) + 5 = 14 + 5 = 19 \] For Leg 2: \[ 3x - 2 = 3(7) - 2 = 21 - 2 = 19 \] Both legs are equal to \( 19 \). Since we have an isosceles triangle, the base length can be determined using the properties of triangles. However, the problem does not provide any information about the base length directly. Given the options: - 9.5 - 7 - Cannot be determined - 19 Since we cannot determine the base length from the information provided, the correct answer is: **Cannot be determined**.