Let us determine which equation can be used to find the value of [tex]\( x \)[/tex] in the given isosceles triangle scenario.
Given:
1. The perimeter of the isosceles triangle is [tex]\( 7.5 \)[/tex] meters.
2. The shortest side [tex]\( y \)[/tex] measures [tex]\( 2.1 \)[/tex] meters.
In an isosceles triangle, two sides are equal. Let [tex]\( x \)[/tex] be the length of each of the two equal sides. Thus, the sides can be represented as [tex]\( x \)[/tex], [tex]\( x \)[/tex], and [tex]\( 2.1 \)[/tex].
The formula for the perimeter of a triangle is the sum of all its sides:
[tex]\[ x + x + 2.1 = 7.5 \][/tex]
Simplifying this, we get:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Now that we have a simplified equation, we can see that the equation which can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
So, the correct equation from the given options is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
