Find B2C2 Length: Comparing Trapezoids with Equal Perimeters of 5-7 Units

To solve this problem, we'll follow these steps:

• Step 1: Calculate the perimeter of Trapezoid 1.
• Step 2: Set the perimeters of the trapezoids equal to each other.
• Step 3: Solve the equation for the unknown length $B2C2$.

Now, let's work through each step:
Step 1: The perimeter of Trapezoid 1 is given by the sum: $P_1 = 5 + 6 + 7 + X = 18 + X$
Step 2: Assume the perimeter of Trapezoid 2 is the same: $P_2 = 5 + 7 + X + B2C2 = 12 + X + B2C2$
Step 3: Equate $P_1$ and $P_2$: $18 + X = 12 + X + B2C2$ Subtract $X$ from both sides: $18 = 12 + B2C2$ Finally, solve for $B2C2$: $B2C2 = 18 - 12 = 6$

Therefore, the solution to the problem is $B2C2 = 6$.