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Answer :
To solve this problem, we need to find the equation that represents the given conditions of the isosceles triangle.
1. Understanding the Problem:
- We are given an isosceles triangle with a total perimeter of 7.5 meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
- We need to determine which equation correctly represents the situation to find the value of [tex]\( x \)[/tex], the lengths of the other two equal sides.
2. Setting Up the Equation:
- In an isosceles triangle, two sides are of equal length. Let's denote the equal sides as [tex]\( x \)[/tex].
- The perimeter of a triangle is the sum of all its sides.
- Therefore, the perimeter equation for this triangle is: [tex]\( 2x + y = 7.5 \)[/tex].
3. Substituting the Known Values:
- We know that the shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute [tex]\( y = 2.1 \)[/tex] into the perimeter equation:
[tex]\( 2x + 2.1 = 7.5 \)[/tex].
4. Selecting the Correct Equation:
- From the options given:
- [tex]$2 x - 2.1 = 7.5$[/tex]
- [tex]$4.2 + v = 7.5$[/tex]
- [tex]$y - 4.2 = 7.5$[/tex]
- [tex]$2.1 + 2 x = 7.5$[/tex]
- The equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] properly represents our setup.
5. Solving for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
This means the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and the length of the other two sides [tex]\( x \)[/tex] is 2.7 meters each. Thus, option "[tex]$2.1 + 2 x = 7.5$[/tex]" is the equation we are looking for.
1. Understanding the Problem:
- We are given an isosceles triangle with a total perimeter of 7.5 meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures 2.1 meters.
- We need to determine which equation correctly represents the situation to find the value of [tex]\( x \)[/tex], the lengths of the other two equal sides.
2. Setting Up the Equation:
- In an isosceles triangle, two sides are of equal length. Let's denote the equal sides as [tex]\( x \)[/tex].
- The perimeter of a triangle is the sum of all its sides.
- Therefore, the perimeter equation for this triangle is: [tex]\( 2x + y = 7.5 \)[/tex].
3. Substituting the Known Values:
- We know that the shortest side [tex]\( y \)[/tex] is 2.1 meters.
- Substitute [tex]\( y = 2.1 \)[/tex] into the perimeter equation:
[tex]\( 2x + 2.1 = 7.5 \)[/tex].
4. Selecting the Correct Equation:
- From the options given:
- [tex]$2 x - 2.1 = 7.5$[/tex]
- [tex]$4.2 + v = 7.5$[/tex]
- [tex]$y - 4.2 = 7.5$[/tex]
- [tex]$2.1 + 2 x = 7.5$[/tex]
- The equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] properly represents our setup.
5. Solving for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
This means the correct equation is [tex]\( 2.1 + 2x = 7.5 \)[/tex], and the length of the other two sides [tex]\( x \)[/tex] is 2.7 meters each. Thus, option "[tex]$2.1 + 2 x = 7.5$[/tex]" is the equation we are looking for.
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