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Answer :
To solve the problem of finding the equation for the value of [tex]\( x \)[/tex] in the isosceles triangle, let's break it down step-by-step:
1. Identify the known values:
- The perimeter of the triangle is 7.5 meters.
- The length of the shortest side, [tex]\( y \)[/tex], is 2.1 meters.
2. Understand the properties of an isosceles triangle:
- In an isosceles triangle, two sides are of equal length. Let's denote this length as [tex]\( x \)[/tex].
3. Set up the equation using the perimeter:
- The perimeter of the triangle is the sum of all its sides. For our isosceles triangle, this can be expressed as:
[tex]\[
x + x + y = 7.5
\][/tex]
- Since [tex]\( y = 2.1 \)[/tex], we substitute this value into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
4. Simplify the equation:
- Combine the terms with [tex]\( x \)[/tex]:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
So, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This equation reflects that the sum of the two equal sides [tex]\( x \)[/tex] and the shortest side [tex]\( y \)[/tex] equals the total perimeter of the triangle.
1. Identify the known values:
- The perimeter of the triangle is 7.5 meters.
- The length of the shortest side, [tex]\( y \)[/tex], is 2.1 meters.
2. Understand the properties of an isosceles triangle:
- In an isosceles triangle, two sides are of equal length. Let's denote this length as [tex]\( x \)[/tex].
3. Set up the equation using the perimeter:
- The perimeter of the triangle is the sum of all its sides. For our isosceles triangle, this can be expressed as:
[tex]\[
x + x + y = 7.5
\][/tex]
- Since [tex]\( y = 2.1 \)[/tex], we substitute this value into the equation:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
4. Simplify the equation:
- Combine the terms with [tex]\( x \)[/tex]:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
So, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This equation reflects that the sum of the two equal sides [tex]\( x \)[/tex] and the shortest side [tex]\( y \)[/tex] equals the total perimeter of the triangle.
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