Answer :
Sure! Let's solve the problem step-by-step.
1. Understanding the Problem:
- We are given that we have an isosceles triangle.
- The perimeter of this triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
- We need to find an equation to solve for [tex]\( x \)[/tex], which represents the lengths of the other two equal sides of the triangle.
2. Setting Up the Equation:
- For an isosceles triangle, two sides are of equal length, and the third side is different (here it's given as the shortest side [tex]\( y \)[/tex]).
- Let's denote the lengths of the equal sides as [tex]\( x \)[/tex].
3. Formulating the Perimeter Equation:
- The perimeter of the triangle is the sum of all its sides.
- The formula for the perimeter of our isosceles triangle here will be:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying this, we get:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substituting the Known Value:
- We are given that [tex]\( y = 2.1 \)[/tex].
- Substitute [tex]\( y \)[/tex] in the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
So, the equation we can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Thus, the correct option from the provided choices is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
1. Understanding the Problem:
- We are given that we have an isosceles triangle.
- The perimeter of this triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
- We need to find an equation to solve for [tex]\( x \)[/tex], which represents the lengths of the other two equal sides of the triangle.
2. Setting Up the Equation:
- For an isosceles triangle, two sides are of equal length, and the third side is different (here it's given as the shortest side [tex]\( y \)[/tex]).
- Let's denote the lengths of the equal sides as [tex]\( x \)[/tex].
3. Formulating the Perimeter Equation:
- The perimeter of the triangle is the sum of all its sides.
- The formula for the perimeter of our isosceles triangle here will be:
[tex]\[
x + x + y = 7.5
\][/tex]
Simplifying this, we get:
[tex]\[
2x + y = 7.5
\][/tex]
4. Substituting the Known Value:
- We are given that [tex]\( y = 2.1 \)[/tex].
- Substitute [tex]\( y \)[/tex] in the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
So, the equation we can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Thus, the correct option from the provided choices is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
