Answer :
Let's solve this step-by-step.
Given:
- The perimeter of the isosceles triangle is [tex]\(7.5\)[/tex] meters.
- The shortest side ([tex]\(y\)[/tex]) measures [tex]\(2.1\)[/tex] meters.
In an isosceles triangle, two sides are equal in length, and one side is different. Let’s denote:
- [tex]\(x\)[/tex] as the length of the two equal sides.
- [tex]\(y\)[/tex] as the length of the shortest side.
The formula for the perimeter of the isosceles triangle is:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Substitute the given values into the perimeter equation:
[tex]\[ 7.5 = x + x + 2.1 \][/tex]
Simplify the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
Rewrite the equation to isolate [tex]\(2x\)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This matches one of the given options:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation can be used to find the value of [tex]\(x\)[/tex].
Given:
- The perimeter of the isosceles triangle is [tex]\(7.5\)[/tex] meters.
- The shortest side ([tex]\(y\)[/tex]) measures [tex]\(2.1\)[/tex] meters.
In an isosceles triangle, two sides are equal in length, and one side is different. Let’s denote:
- [tex]\(x\)[/tex] as the length of the two equal sides.
- [tex]\(y\)[/tex] as the length of the shortest side.
The formula for the perimeter of the isosceles triangle is:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Substitute the given values into the perimeter equation:
[tex]\[ 7.5 = x + x + 2.1 \][/tex]
Simplify the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
Rewrite the equation to isolate [tex]\(2x\)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This matches one of the given options:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This equation can be used to find the value of [tex]\(x\)[/tex].
