Isosceles Trapezoid Problem: Finding C2D2 Length in Equal Shapes

Question

The two trapezoids below are isosceles.

What is the size of C2D2 if the trapezoids are equal?

00:00 Find side C2D2

00:03 Let's start by calculating the perimeter of trapezoid 1

00:07 The perimeter of the trapezoid equals the sum of its sides

00:10 Let's substitute appropriate values according to the given data and solve for the perimeter

00:15 This is the perimeter size of trapezoid 1

00:18 Now we'll use this size to find side C2D2

00:22 Let's substitute appropriate values in the perimeter formula and solve for the side

00:38 Let's substitute the perimeter size in the equation to find the side

00:46 Let's isolate side C2D2

01:05 And this is the solution to the problem

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

For the first trapezoid $A_1B_1C_1D_1$ :

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

For the second trapezoid $A_2B_2C_2D_2$ :

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 $2X - 4$ .

2X-4