Answer :
To solve the problem regarding the isosceles triangle's perimeter, let's break it down step-by-step:
1. Understanding the Problem:
- We have an isosceles triangle, which means two of its sides are of equal length.
- The perimeter of the triangle is given as 7.5 meters.
- The shortest side is given as 2.1 meters. We'll label this side as [tex]\( y = 2.1 \)[/tex] meters.
2. Identifying the Unknowns:
- Let the length of each of the equal sides be [tex]\( x \)[/tex].
3. Setting Up the Equation:
- The formula for the perimeter of a triangle is the sum of the lengths of its three sides.
- For an isosceles triangle with two equal sides, the equation can be written as:
[tex]\[
x + x + y = \text{Perimeter}
\][/tex]
4. Plugging in the Given Values:
- We know:
- [tex]\( y = 2.1 \)[/tex] meters
- Perimeter = 7.5 meters
- Substitute these values into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- This simplifies to:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Finding the Equation:
- The equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] represents the relationship that will allow us to solve for [tex]\( x \)[/tex].
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
1. Understanding the Problem:
- We have an isosceles triangle, which means two of its sides are of equal length.
- The perimeter of the triangle is given as 7.5 meters.
- The shortest side is given as 2.1 meters. We'll label this side as [tex]\( y = 2.1 \)[/tex] meters.
2. Identifying the Unknowns:
- Let the length of each of the equal sides be [tex]\( x \)[/tex].
3. Setting Up the Equation:
- The formula for the perimeter of a triangle is the sum of the lengths of its three sides.
- For an isosceles triangle with two equal sides, the equation can be written as:
[tex]\[
x + x + y = \text{Perimeter}
\][/tex]
4. Plugging in the Given Values:
- We know:
- [tex]\( y = 2.1 \)[/tex] meters
- Perimeter = 7.5 meters
- Substitute these values into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- This simplifies to:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Finding the Equation:
- The equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] represents the relationship that will allow us to solve for [tex]\( x \)[/tex].
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
