Answer :
Let's denote the two equal sides by [tex]$x$[/tex] and the base (shortest side) by [tex]$y$[/tex]. The perimeter [tex]$P$[/tex] of the isosceles triangle is given by
[tex]$$
2x + y = 7.5.
$$[/tex]
Since we are told that the shortest side measures [tex]$2.1\text{ m}$[/tex], we substitute [tex]$y=2.1$[/tex] into the equation:
[tex]$$
2x + 2.1 = 7.5.
$$[/tex]
This is the equation that can be used to find the value of [tex]$x$[/tex]. Next, if we want to find [tex]$x$[/tex], we subtract [tex]$2.1$[/tex] from both sides:
[tex]$$
2x = 7.5 - 2.1 = 5.4.
$$[/tex]
Then, by dividing both sides by [tex]$2$[/tex], we find:
[tex]$$
x = \frac{5.4}{2} = 2.7.
$$[/tex]
So, the equation corresponding to the triangle's dimensions is
[tex]$$
2.1 + 2x = 7.5.
$$[/tex]
Thus, the correct option is the fourth one.
[tex]$$
2x + y = 7.5.
$$[/tex]
Since we are told that the shortest side measures [tex]$2.1\text{ m}$[/tex], we substitute [tex]$y=2.1$[/tex] into the equation:
[tex]$$
2x + 2.1 = 7.5.
$$[/tex]
This is the equation that can be used to find the value of [tex]$x$[/tex]. Next, if we want to find [tex]$x$[/tex], we subtract [tex]$2.1$[/tex] from both sides:
[tex]$$
2x = 7.5 - 2.1 = 5.4.
$$[/tex]
Then, by dividing both sides by [tex]$2$[/tex], we find:
[tex]$$
x = \frac{5.4}{2} = 2.7.
$$[/tex]
So, the equation corresponding to the triangle's dimensions is
[tex]$$
2.1 + 2x = 7.5.
$$[/tex]
Thus, the correct option is the fourth one.
