Answer :
Sure! Let's go through the process of finding the correct equation to determine the value of [tex]\( x \)[/tex] step-by-step.
1. Understanding the Problem:
- The triangle is isosceles, meaning it has two sides of equal length.
- The perimeter of the triangle is 7.5 meters.
- The shortest side of the triangle, [tex]\( y \)[/tex], is given as 2.1 meters.
2. Setting Up the Problem:
- In an isosceles triangle, if we let the two equal sides be [tex]\( x \)[/tex] each, then the sides of the triangle are [tex]\( x \)[/tex], [tex]\( x \)[/tex], and [tex]\( 2.1 \)[/tex] meters.
3. Writing the Perimeter Equation:
- The perimeter of the triangle is the sum of its three sides.
- Therefore, the perimeter can be written as:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
4. Simplifying the Equation:
- Combine like terms [tex]\( x + x \)[/tex] to get [tex]\( 2x \)[/tex]:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Identifying the Correct Equation:
- From the list of provided equations:
[tex]\[
2 x - 2.1 = 7.5
\][/tex]
[tex]\[
4.2 + y = 7.5
\][/tex]
[tex]\[
y - 4.2 = 7.5
\][/tex]
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
- The correct equation that matches our simplified equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] is:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
So, the equation you can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
That's the detailed solution for the given problem.
1. Understanding the Problem:
- The triangle is isosceles, meaning it has two sides of equal length.
- The perimeter of the triangle is 7.5 meters.
- The shortest side of the triangle, [tex]\( y \)[/tex], is given as 2.1 meters.
2. Setting Up the Problem:
- In an isosceles triangle, if we let the two equal sides be [tex]\( x \)[/tex] each, then the sides of the triangle are [tex]\( x \)[/tex], [tex]\( x \)[/tex], and [tex]\( 2.1 \)[/tex] meters.
3. Writing the Perimeter Equation:
- The perimeter of the triangle is the sum of its three sides.
- Therefore, the perimeter can be written as:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
4. Simplifying the Equation:
- Combine like terms [tex]\( x + x \)[/tex] to get [tex]\( 2x \)[/tex]:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
5. Identifying the Correct Equation:
- From the list of provided equations:
[tex]\[
2 x - 2.1 = 7.5
\][/tex]
[tex]\[
4.2 + y = 7.5
\][/tex]
[tex]\[
y - 4.2 = 7.5
\][/tex]
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
- The correct equation that matches our simplified equation [tex]\( 2x + 2.1 = 7.5 \)[/tex] is:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
So, the equation you can use to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2 x = 7.5
\][/tex]
That's the detailed solution for the given problem.
