Answer :
Sure, let's solve this problem step-by-step.
We have an isosceles triangle with a given perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length, and the third side can be different. In this problem, we are told that the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. We need to find an equation that helps us determine the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the length of each of the two equal sides.
To solve this:
1. Understand the Perimeter Formula:
The perimeter of a triangle is the sum of the lengths of all three sides. For this isosceles triangle, the perimeter can be expressed as:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
where [tex]\( 2x \)[/tex] represents the two equal sides and [tex]\( y \)[/tex] is the shortest side.
2. Substitute the Known Values:
We know the perimeter is 7.5 meters and the shortest side [tex]\( y \)[/tex] is 2.1 meters. Plug these values into the perimeter equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find the equation that represents this situation, we need to isolate [tex]\( x \)[/tex]:
- First, subtract 2.1 from both sides of the equation:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
This simplifies to:
[tex]\[
5.4 = 2x
\][/tex]
4. Equation to Find [tex]\( x \)[/tex]:
Now, the equation [tex]\( 2x = 5.4 \)[/tex] can be used to find the value of [tex]\( x \)[/tex].
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] given the perimeter is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This corresponds to the last option in the list.
We have an isosceles triangle with a given perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length, and the third side can be different. In this problem, we are told that the shortest side, [tex]\( y \)[/tex], measures 2.1 meters. We need to find an equation that helps us determine the value of [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the length of each of the two equal sides.
To solve this:
1. Understand the Perimeter Formula:
The perimeter of a triangle is the sum of the lengths of all three sides. For this isosceles triangle, the perimeter can be expressed as:
[tex]\[
\text{Perimeter} = 2x + y
\][/tex]
where [tex]\( 2x \)[/tex] represents the two equal sides and [tex]\( y \)[/tex] is the shortest side.
2. Substitute the Known Values:
We know the perimeter is 7.5 meters and the shortest side [tex]\( y \)[/tex] is 2.1 meters. Plug these values into the perimeter equation:
[tex]\[
7.5 = 2x + 2.1
\][/tex]
3. Isolate [tex]\( x \)[/tex]:
To find the equation that represents this situation, we need to isolate [tex]\( x \)[/tex]:
- First, subtract 2.1 from both sides of the equation:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]
This simplifies to:
[tex]\[
5.4 = 2x
\][/tex]
4. Equation to Find [tex]\( x \)[/tex]:
Now, the equation [tex]\( 2x = 5.4 \)[/tex] can be used to find the value of [tex]\( x \)[/tex].
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] given the perimeter is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This corresponds to the last option in the list.
