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Answer :
To solve this problem, let's break it down step by step. We have an isosceles triangle with a known perimeter and one known side, and we need to find an equation to determine the variable [tex]\( x \)[/tex], which represents the other two sides.
1. Understanding Isosceles Triangle: An isosceles triangle has two sides of equal length. In this problem, let's assume the two equal sides are [tex]\( x \)[/tex].
2. Given Information:
- Perimeter of the triangle = 7.5 meters.
- Shortest side [tex]\( y \)[/tex] = 2.1 meters.
3. Formulating the Perimeter Equation:
- The perimeter of a triangle is the sum of all its sides. For this triangle:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
4. Substitute the known values:
- We know the perimeter is 7.5 meters and [tex]\( y \)[/tex] is 2.1 meters. This gives us the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This equation, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the correct one to use to find the value of [tex]\( x \)[/tex].
1. Understanding Isosceles Triangle: An isosceles triangle has two sides of equal length. In this problem, let's assume the two equal sides are [tex]\( x \)[/tex].
2. Given Information:
- Perimeter of the triangle = 7.5 meters.
- Shortest side [tex]\( y \)[/tex] = 2.1 meters.
3. Formulating the Perimeter Equation:
- The perimeter of a triangle is the sum of all its sides. For this triangle:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
4. Substitute the known values:
- We know the perimeter is 7.5 meters and [tex]\( y \)[/tex] is 2.1 meters. This gives us the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This equation, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the correct one to use to find the value of [tex]\( x \)[/tex].
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