Perimeter of a Trapezoid: Comparison between 2 of the same shape with an identical perimeter

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 $B2C2 = 6$.

To find the solution, we begin by calculating the perimeters of each trapezoid:

For trapezoid $A$, the sides are $4$, $7$, $7$, and $5$. Therefore, the perimeter $pA$ is:

$pA = 4 + 7 + 7 + 5 = 23$

For trapezoid $B$, the sides are $2$, $7$, $11$, and $3$. Thus, the perimeter $pB$ is:

$pB = 2 + 7 + 11 + 3 = 23$

Both trapezoids have identical perimeters of $23$. However, their areas cannot be determined to be identical without information about the heights of the trapezoids. Since these are crucial for the area calculation, the equivalence of their areas cannot be concluded from available data.

Therefore, the perimeter is $pA = pB = 23$, but their areas are not necessarily identical.

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 $2X - 4$.

We calculate the perimeter of the left trapezoid:

$P=10+12+x+y$

$P=22+x+y$

We calculate the perimeterof the right trapezoid:

$P=x+5+17+\frac{y}{3}+\frac{2y}{3}$

$P=x+22+\frac{2y+y}{3}$

$P=x+22+\frac{3y}{3}$

$P=x+22+y$

It can be seen that the two perimeters are identical to each other.

We calculate the perimeter of the left trapezoid:

$P=6+10+7+\frac{5}{2}x+5$

$P=28+\frac{5}{2}x$

We calculate the perimeter of the right trapezoid:

$P=7+x+x+16+\frac{x}{2}+5$

$P=2\frac{1}{2}x+28$

$P=\frac{5}{2}x+28$

The perimeters of the two trapezoids are equal to each other.

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

• Step 1: Calculate the perimeter of each trapezoid
• Step 2: Set the perimeters equal to each other
• Step 3: Solve for $X$

Let's work through the steps:

Step 1: Calculate the perimeter of each trapezoid.

For the first trapezoid, the perimeter is:

$5X + (2X - 2) + (X - 1) + 6X = 14X - 3$

For the second trapezoid, the perimeter is:

$(2X + 1) + 4X + (4X + 1) + 3X = 13X + 2$

Step 2: Set the two perimeter expressions equal:

$14X - 3 = 13X + 2$

Step 3: Solve for $X$.

Subtract $13X$ from both sides:

$X - 3 = 2$

Add 3 to both sides:

$X = 5$

Therefore, the solution to the problem is $X = 5$.