Solve for X: Trapezoid Perimeter with Side Lengths 10x+5 and 10x+4

To calculate $x$ in the trapezoid, start by using the formula for the perimeter, which is the sum of all sides.

The given sides of the trapezoid are: - One side as $10x + 5$ - Another side as $10x + 4$ - A third side as $x + 2$ - The fourth side as $x$

The formula for the perimeter is: $P = (10x + 5) + (10x + 4) + (x + 2) + x$

Substitute the given perimeter, 55, into the equation:

$55 = (10x + 5) + (10x + 4) + (x + 2) + x$

Simplify the equation by combining like terms:

$55 = 10x + 5 + 10x + 4 + x + 2 + x$

$55 = 22x + 11$

Subtract 11 from both sides to isolate terms involving $x$:

$44 = 22x$

Divide both sides by 22 to solve for $x$:

$x = 2$

Thus, the value of $x$ that satisfies the equation is $\boxed{2}$.