Isosceles Trapezoid Problem: Finding C2D2 Length in Equal Shapes

To solve this problem, let's calculate the perimeters of both trapezoids:

For the first trapezoid $A_1B_1C_1D_1$:

• Top base: $A_1B_1 = 2X$
• Bottom base: $C_1D_1 = 3X$
• Two equal side extensions, each of length 4.

The perimeter $P_1$ of the first trapezoid is:
$P_1 = 2X + 3X + 4 + 4 = 5X + 8$.

For the second trapezoid $A_2B_2C_2D_2$:

• Top base: $A_2B_2 = 3X$
• Bottom base: $C_2D_2 = ?$
• Two equal side extensions, each of length 6.

The perimeter $P_2$ of the second trapezoid is:
$P_2 = 3X + C_2D_2 + 6 + 6 = 3X + C_2D_2 + 12$.

Since the trapezoids are equal, their perimeters are the same:
$5X + 8 = 3X + C_2D_2 + 12$.

Solving for $C_2D_2$:

$C_2D_2 = 5X + 8 - 3X - 12$

$C_2D_2 = 2X - 4$

Thus, the size of $C_2D_2$ if the trapezoids are equal is $2X - 4$.