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Answer :
To solve this problem, let's start by understanding the setup of the isosceles triangle:
1. Isosceles Triangle Definition: An isosceles triangle has two sides that are equal.
2. Given Information:
- The perimeter of the triangle is 7.5 meters.
- The shortest side of the triangle, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
3. Requirements:
- We need to find the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] represents the length of each of the equal sides.
4. Formulating the Equation:
- Since it is an isosceles triangle, two sides are equal, and the shortest side is different. Therefore, we can assume the other sides are each [tex]\( x \)[/tex] meters long.
- The formula for the perimeter of this triangle is:
[tex]\[
x + x + y = \text{perimeter}
\][/tex]
- Substituting the given values, the equation becomes:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Solving the Equation:
- Subtract 2.1 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Based on this solution, the equation we used to find [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, the correct choice is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
1. Isosceles Triangle Definition: An isosceles triangle has two sides that are equal.
2. Given Information:
- The perimeter of the triangle is 7.5 meters.
- The shortest side of the triangle, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
3. Requirements:
- We need to find the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] represents the length of each of the equal sides.
4. Formulating the Equation:
- Since it is an isosceles triangle, two sides are equal, and the shortest side is different. Therefore, we can assume the other sides are each [tex]\( x \)[/tex] meters long.
- The formula for the perimeter of this triangle is:
[tex]\[
x + x + y = \text{perimeter}
\][/tex]
- Substituting the given values, the equation becomes:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Solving the Equation:
- Subtract 2.1 from both sides to isolate the terms involving [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Based on this solution, the equation we used to find [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
Therefore, the correct choice is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
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