The problem asks us to find the value of $x$ given that the perimeter $P$ of the trapezoid is 41 yards. The lengths of the sides are given as $2x-1$, $2x$, $x$, and $2x$.

1. Problem Description

The problem asks us to find the value of $x$ given that the perimeter $P$ of the trapezoid is 41 yards. The lengths of the sides are given as $2x-1$, $2x$, $x$, and $2x$.

2. Solution Steps

The perimeter of the trapezoid is the sum of the lengths of its sides. Thus, we have:

$P = (2x - 1) + 2x + x + 2x$

We are given that $P = 41$. Substituting this value into the equation above, we get:

$41 = (2x - 1) + 2x + x + 2x$

Combining like terms, we have:

$41 = 7x - 1$

Adding 1 to both sides of the equation, we get:

$41 + 1 = 7x - 1 + 1$

$42 = 7x$

Dividing both sides by 7, we find:

$\frac{42}{7} = \frac{7x}{7}$

$6 = x$

3. Final Answer

$x = 6$