Answer :
To solve the problem, let's start by understanding the situation.
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length. Let's assume these equal sides measure [tex]\(x\)[/tex] meters each. We're given that the shortest side, [tex]\(y\)[/tex], is 2.1 meters.
The perimeter of the triangle is the sum of all its sides:
[tex]\[
x + x + y = 7.5
\][/tex]
[tex]\[
2x + y = 7.5
\][/tex]
Since we know the value of the shortest side [tex]\(y\)[/tex] is 2.1 meters, we substitute that into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Now, we need to solve for [tex]\(x\)[/tex] by isolating it on one side of the equation. First, subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
Perform the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Next, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
Calculate the division:
[tex]\[
x = 2.7
\][/tex]
Therefore, the equation from the options provided that can be used to find the value of [tex]\(x\)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
The correct equation that matches this setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length. Let's assume these equal sides measure [tex]\(x\)[/tex] meters each. We're given that the shortest side, [tex]\(y\)[/tex], is 2.1 meters.
The perimeter of the triangle is the sum of all its sides:
[tex]\[
x + x + y = 7.5
\][/tex]
[tex]\[
2x + y = 7.5
\][/tex]
Since we know the value of the shortest side [tex]\(y\)[/tex] is 2.1 meters, we substitute that into the perimeter equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
Now, we need to solve for [tex]\(x\)[/tex] by isolating it on one side of the equation. First, subtract 2.1 from both sides:
[tex]\[
2x = 7.5 - 2.1
\][/tex]
Perform the subtraction:
[tex]\[
2x = 5.4
\][/tex]
Next, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
Calculate the division:
[tex]\[
x = 2.7
\][/tex]
Therefore, the equation from the options provided that can be used to find the value of [tex]\(x\)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
The correct equation that matches this setup is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]
