Answer :
We are given an isosceles triangle with a perimeter of [tex]$7.5\text{ m}$[/tex] and the shortest side [tex]$y = 2.1\text{ m}$[/tex]. In an isosceles triangle, the other two sides are equal in length. If we denote the length of each of these equal sides by [tex]$x$[/tex], the perimeter is the sum of all the sides:
[tex]$$
y + x + x = y + 2x = 7.5
$$[/tex]
Substituting [tex]$y = 2.1$[/tex] into the equation, we have:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]
This is the equation that can be used to find the value of [tex]$x$[/tex]. Thus, the correct option is:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]
For clarity, solving for [tex]$x$[/tex] would follow these steps:
1. Subtract [tex]$2.1$[/tex] from both sides:
[tex]$$
2x = 7.5 - 2.1 = 5.4
$$[/tex]
2. Divide both sides by [tex]$2$[/tex]:
[tex]$$
x = \frac{5.4}{2} = 2.7
$$[/tex]
So, the other two sides each measure [tex]$2.7\text{ m}$[/tex].
Therefore, the equation used to find the value of [tex]$x$[/tex] is:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]
[tex]$$
y + x + x = y + 2x = 7.5
$$[/tex]
Substituting [tex]$y = 2.1$[/tex] into the equation, we have:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]
This is the equation that can be used to find the value of [tex]$x$[/tex]. Thus, the correct option is:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]
For clarity, solving for [tex]$x$[/tex] would follow these steps:
1. Subtract [tex]$2.1$[/tex] from both sides:
[tex]$$
2x = 7.5 - 2.1 = 5.4
$$[/tex]
2. Divide both sides by [tex]$2$[/tex]:
[tex]$$
x = \frac{5.4}{2} = 2.7
$$[/tex]
So, the other two sides each measure [tex]$2.7\text{ m}$[/tex].
Therefore, the equation used to find the value of [tex]$x$[/tex] is:
[tex]$$
2.1 + 2x = 7.5
$$[/tex]