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Answer :
To solve this problem, we need to find an equation to determine the value of [tex]\(x\)[/tex], given that the isosceles triangle has a perimeter of 7.5 meters and its shortest side [tex]\(y\)[/tex] measures 2.1 meters.
In an isosceles triangle, two sides are equal in length. Let's assume that the two equal sides are of length [tex]\(x\)[/tex].
### Step-by-step Solution:
1. Understand the Perimeter:
- The perimeter of a triangle is the sum of all its sides.
- Here, the perimeter is given as 7.5 meters.
2. Identify the Sides:
- The triangle has two equal sides (each of length [tex]\(x\)[/tex]).
- The shortest side [tex]\(y\)[/tex] is given as 2.1 meters.
3. Set up the Perimeter Equation:
- The formula for the perimeter of the triangle will be:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- Substitute the given [tex]\(y = 2.1\)[/tex] into the formula:
[tex]\[
\text{Perimeter} = x + x + 2.1 = 2x + 2.1
\][/tex]
4. Match Perimeter with the Given Value:
- We know the perimeter is 7.5 meters, so we set up the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Check the Corresponding Equation:
- The equation that matches the given conditions is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\(x\)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
In an isosceles triangle, two sides are equal in length. Let's assume that the two equal sides are of length [tex]\(x\)[/tex].
### Step-by-step Solution:
1. Understand the Perimeter:
- The perimeter of a triangle is the sum of all its sides.
- Here, the perimeter is given as 7.5 meters.
2. Identify the Sides:
- The triangle has two equal sides (each of length [tex]\(x\)[/tex]).
- The shortest side [tex]\(y\)[/tex] is given as 2.1 meters.
3. Set up the Perimeter Equation:
- The formula for the perimeter of the triangle will be:
[tex]\[
\text{Perimeter} = x + x + y
\][/tex]
- Substitute the given [tex]\(y = 2.1\)[/tex] into the formula:
[tex]\[
\text{Perimeter} = x + x + 2.1 = 2x + 2.1
\][/tex]
4. Match Perimeter with the Given Value:
- We know the perimeter is 7.5 meters, so we set up the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Check the Corresponding Equation:
- The equation that matches the given conditions is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the equation that can be used to find the value of [tex]\(x\)[/tex] is [tex]\(2.1 + 2x = 7.5\)[/tex].
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