Answer :
To find the value of [tex]\( x \)[/tex] for the isosceles triangle, we are given the following information:
- The total perimeter of the triangle is 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
- We are dealing with an isosceles triangle, which means it has two equal sides.
Given these points, let's follow the steps to find the equation and solve it:
1. Identify the sides: In an isosceles triangle, there are two equal sides. Let's call the length of each equal side [tex]\( x \)[/tex].
2. Express the perimeter: The formula for the perimeter of a triangle is the sum of its three sides. Therefore, the perimeter of this isosceles triangle can be written as:
[tex]\[
x + x + y = 7.5
\][/tex]
This simplifies to:
[tex]\[
2x + y = 7.5
\][/tex]
3. Substitute the known value of [tex]\( y \)[/tex]: We are given [tex]\( y = 2.1 \)[/tex]. Substituting this value into the equation gives:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- First, move 2.1 to the other side of the equation by subtracting it from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the right side:
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
The correct equation from the given options that matches our setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 2.7 meters, and the correct equation to use is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
- The total perimeter of the triangle is 7.5 meters.
- The shortest side, [tex]\( y \)[/tex], measures 2.1 meters.
- We are dealing with an isosceles triangle, which means it has two equal sides.
Given these points, let's follow the steps to find the equation and solve it:
1. Identify the sides: In an isosceles triangle, there are two equal sides. Let's call the length of each equal side [tex]\( x \)[/tex].
2. Express the perimeter: The formula for the perimeter of a triangle is the sum of its three sides. Therefore, the perimeter of this isosceles triangle can be written as:
[tex]\[
x + x + y = 7.5
\][/tex]
This simplifies to:
[tex]\[
2x + y = 7.5
\][/tex]
3. Substitute the known value of [tex]\( y \)[/tex]: We are given [tex]\( y = 2.1 \)[/tex]. Substituting this value into the equation gives:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- First, move 2.1 to the other side of the equation by subtracting it from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
- Simplify the right side:
[tex]\[
2x = 5.4
\][/tex]
- Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5.4}{2} = 2.7
\][/tex]
The correct equation from the given options that matches our setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 2.7 meters, and the correct equation to use is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
