Find X in a Parallelogram: Using Perimeter P=54 and Side Length 7

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

• Step 1: Identify the known value of one side and the perimeter.
• Step 2: Use the perimeter formula to set up an equation.
• Step 3: Solve for the unknown side $x$.

Now, let's work through each step:
Step 1: The problem gives us a perimeter $P = 54$ and one side of the parallelogram as 7.
Step 2: Using the formula for the perimeter of a parallelogram $P = 2(a + b)$, we have:

$2(x + 7) = 54$

Step 3: Simplify and solve for $x$:

Divide both sides by 2:

$x + 7 = 27$

Subtract 7 from both sides to isolate $x$:

$x = 27 - 7$

Simplifying, we obtain:

$x = 20$

Therefore, the solution to the problem is $x = 20$.