Answer :
To solve the problem, we need to find the correct equation that represents the perimeter of the isosceles triangle, given the values provided.
### Understanding the Problem:
- We have an isosceles triangle, meaning two sides are of equal length, and one side is different.
- The triangle's perimeter is 7.5 meters.
- The shortest side of the triangle is given as [tex]\( y = 2.1 \)[/tex] meters.
### Finding the Equation:
1. Identify the Triangle Sides:
- In an isosceles triangle, the two sides that are equal can be represented as [tex]\( x \)[/tex].
- The shortest side is [tex]\( y = 2.1 \)[/tex].
2. Perimeter Calculation:
- The perimeter of the triangle is the sum of all its sides. Therefore, the formula for the perimeter [tex]\( P \)[/tex] is:
[tex]\[
P = x + x + y = 2x + y
\][/tex]
3. Set the Equation for the Given Perimeter:
- We know the perimeter is 7.5 meters, so we can set up the equation as follows:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This matches the option: [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, this is the correct equation to use for finding [tex]\( x \)[/tex].
### Understanding the Problem:
- We have an isosceles triangle, meaning two sides are of equal length, and one side is different.
- The triangle's perimeter is 7.5 meters.
- The shortest side of the triangle is given as [tex]\( y = 2.1 \)[/tex] meters.
### Finding the Equation:
1. Identify the Triangle Sides:
- In an isosceles triangle, the two sides that are equal can be represented as [tex]\( x \)[/tex].
- The shortest side is [tex]\( y = 2.1 \)[/tex].
2. Perimeter Calculation:
- The perimeter of the triangle is the sum of all its sides. Therefore, the formula for the perimeter [tex]\( P \)[/tex] is:
[tex]\[
P = x + x + y = 2x + y
\][/tex]
3. Set the Equation for the Given Perimeter:
- We know the perimeter is 7.5 meters, so we can set up the equation as follows:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Thus, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This matches the option: [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, this is the correct equation to use for finding [tex]\( x \)[/tex].
