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Answer :
To find the equation that can be used to determine the value of [tex]\( x \)[/tex] for the isosceles triangle:
1. Understand the structure of the triangle: An isosceles triangle has two equal sides and one different side. Here, we are given a shortest side [tex]\( y \)[/tex] which measures 2.1 meters.
2. Understand the given information:
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
3. Formulate the perimeter equation:
- In an isosceles triangle, if the two equal sides are [tex]\( x \)[/tex], the perimeter can be expressed as:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
4. Substitute the known values into the equation:
- Substitute the perimeter (7.5 meters) and the shortest side [tex]\( y \)[/tex] (2.1 meters) into the perimeter expression:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
5. Identify the equation:
- This equation rearranges to [tex]\( 2.1 + 2x = 7.5 \)[/tex].
So, the correct equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
1. Understand the structure of the triangle: An isosceles triangle has two equal sides and one different side. Here, we are given a shortest side [tex]\( y \)[/tex] which measures 2.1 meters.
2. Understand the given information:
- The perimeter of the triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] is 2.1 meters.
3. Formulate the perimeter equation:
- In an isosceles triangle, if the two equal sides are [tex]\( x \)[/tex], the perimeter can be expressed as:
[tex]\[
\text{Perimeter} = x + x + y = 2x + y
\][/tex]
4. Substitute the known values into the equation:
- Substitute the perimeter (7.5 meters) and the shortest side [tex]\( y \)[/tex] (2.1 meters) into the perimeter expression:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
5. Identify the equation:
- This equation rearranges to [tex]\( 2.1 + 2x = 7.5 \)[/tex].
So, the correct equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
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