Final answer:
To find the perimeter of a rhombus given two expressions for its sides, equate the expressions to solve for x, calculate the side length, and then multiply by 4 to get the perimeter. In this case, the perimeter is 56.
Step-by-step explanation:
To find the perimeter of a rhombus, you need to know the length of all four sides. Since a rhombus has four equal sides, if you know the length of one side, you can multiply it by 4 to get the perimeter. In this case, we have two expressions given for the sides: BE = 2x + 4 and BC = 3x - 1. However, they represent the same side of the rhombus and should be equal, so we can set them equal to each other to find the value of x.
Set the two expressions equal: 2x + 4 = 3x - 1. Solving for x gives us x = 5. Now substitute x back into either expression for the side length: BE = 2(5) + 4 = 14. Therefore, the perimeter P of the rhombus is P = 4 × BE = 4 × 14 = 56.