To solve this problem, you need to understand the properties of an isosceles triangle. An isosceles triangle has two sides that are of equal length and a third side that is different. In this problem, we are given that the isosceles triangle has a perimeter of 7.5 meters and the shortest side [tex]\( y \)[/tex] measures 2.1 meters.
Let's denote the equal sides by [tex]\( x \)[/tex] meters each. Therefore, the perimeter of the triangle, which is the sum of all its sides, can be written as:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Given the value of the perimeter (7.5 meters) and the shortest side ([tex]\( y \)[/tex]), we substitute these values into the equation:
[tex]\[ x + x + 2.1 = 7.5 \][/tex]
This equation simplifies to:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Now, let's match this equation to one of the provided options. The equation we derived is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Which corresponds to:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Thus, the correct equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation implies that the answer is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]
