Answer :
To find the value of [tex]\( x \)[/tex] for the given isosceles triangle, let's break it down:
1. Understand the Problem:
- You have an isosceles triangle, which means it has two sides of the same length.
- The perimeter of the triangle is given as 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
2. Set Up the Equation:
- In an isosceles triangle, let the two equal sides be [tex]\( x \)[/tex] each.
- The perimeter of the triangle is the sum of all its sides: [tex]\( 2x + y \)[/tex].
- Therefore, the equation for the perimeter is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
3. Solve the Equation for [tex]\( x \)[/tex]:
- Subtract 2.1 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Based on the given choices, the correct equation that helps find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation correctly represents the relationship between the sides of the triangle and its perimeter. Using this, we've verified that each of the equal sides (x) measures 2.7 meters.
1. Understand the Problem:
- You have an isosceles triangle, which means it has two sides of the same length.
- The perimeter of the triangle is given as 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
2. Set Up the Equation:
- In an isosceles triangle, let the two equal sides be [tex]\( x \)[/tex] each.
- The perimeter of the triangle is the sum of all its sides: [tex]\( 2x + y \)[/tex].
- Therefore, the equation for the perimeter is:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
3. Solve the Equation for [tex]\( x \)[/tex]:
- Subtract 2.1 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
[tex]\[
x = 2.7
\][/tex]
Based on the given choices, the correct equation that helps find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
This equation correctly represents the relationship between the sides of the triangle and its perimeter. Using this, we've verified that each of the equal sides (x) measures 2.7 meters.
