Calculate Isosceles Trapezoid Perimeter: Finding X When AB=5 and CD=10

To determine the perimeter of an isosceles trapezoid ABCD, we must first recognize the properties inherent in the setup.

We are informed that the trapezoid is isosceles, meaning that the non-parallel sides, $AD$ and $BC$, are equal in length. Thus, by relying on the problem, we recognize that:

• The side $AB$ is 5 units long.
• The base $CD$ is 10 units long.
• The side $AC$ is given as $X$, which accordingly indicates that $BD = X$ due to the isosceles property.

With $AD = BC = X$, we can summarize the perimeter formula of the trapezoid as follows:

$P = AB + BC + CD + AD$

This formula simplifies to:

$P = 5 + X + 10 + X$

After combining like terms, we find that the perimeter is:

$P = 15 + 2X$

Thus, the perimeter of the trapezoid ABCD in terms of $X$ is $15 + 2X$.