Let's solve the problem step by step:
1. We know the triangle is isosceles, which means it has two sides of equal length, and let's denote these equal sides as [tex]\( x \)[/tex]. The shortest side is given as [tex]\( y \)[/tex], and it measures 2.1 meters.
2. We are also given that the perimeter of the triangle is 7.5 meters. The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, in this case, the perimeter can be written as:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
3. Substituting the given values into the perimeter expression:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
4. Thus, to find the equation that can be used to determine the value of [tex]\( x \)[/tex], we rearrange the perimeter expression to the standard form:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] given that the shortest side [tex]\( y \)[/tex] measures 2.1 meters is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
