Trapezoid Perimeter: Express in Terms of 5X, 3X, Z, and 3Y

To solve this problem, we'll express the perimeter of the trapezoid by summing up its side lengths:

• Step 1: Identify the given side lengths.

• Step 2: Apply the perimeter formula for the trapezoid.

• Step 3: Simplify the resulting expression.

Let's work through these steps:

Step 1: The trapezoid has the following side lengths:
- Top base: $5X$
- Left side: $3X$
- Bottom base: $Z$
- Right side: $3Y$

Step 2: Apply the perimeter formula:
The perimeter $P$ is given by the sum of all sides:
\begin{equation} $P = 5X + 3X + Z + 3Y$

Step 3: Simplify the expression:
Combine like terms:
$P = (5X + 3X) + Z + 3Y = 8X + 3Y + Z$

Therefore, the perimeter of the trapezoid is expressed as $8X + 3Y + Z$.