Answer :
We are given an isosceles triangle with a perimeter of
[tex]$$7.5\text{ m},$$[/tex]
and the shortest side (base) is
[tex]$$y = 2.1\text{ m}.$$[/tex]
In an isosceles triangle, the two equal sides can be labeled as
[tex]$$x.$$[/tex]
Thus, the perimeter is the sum of the two equal sides and the base, which gives the equation
[tex]$$2x + y = 7.5.$$[/tex]
Since we know that
[tex]$$y = 2.1,$$[/tex]
we substitute this value into the equation:
[tex]$$2x + 2.1 = 7.5.$$[/tex]
This is the correct equation to find the value of [tex]$x$[/tex].
Now, to verify the steps, we rearrange the equation to solve for [tex]$x$[/tex]. Subtract 2.1 from both sides:
[tex]$$2x = 7.5 - 2.1.$$[/tex]
Calculating the right side,
[tex]$$7.5 - 2.1 = 5.4,$$[/tex]
so we have
[tex]$$2x = 5.4.$$[/tex]
Dividing both sides by 2 gives
[tex]$$x = \frac{5.4}{2} = 2.7.$$[/tex]
Thus, the equation used and the calculations confirm that the equation is
[tex]$$2.1 + 2x = 7.5.$$[/tex]
Therefore, the correct equation is option 4.
[tex]$$7.5\text{ m},$$[/tex]
and the shortest side (base) is
[tex]$$y = 2.1\text{ m}.$$[/tex]
In an isosceles triangle, the two equal sides can be labeled as
[tex]$$x.$$[/tex]
Thus, the perimeter is the sum of the two equal sides and the base, which gives the equation
[tex]$$2x + y = 7.5.$$[/tex]
Since we know that
[tex]$$y = 2.1,$$[/tex]
we substitute this value into the equation:
[tex]$$2x + 2.1 = 7.5.$$[/tex]
This is the correct equation to find the value of [tex]$x$[/tex].
Now, to verify the steps, we rearrange the equation to solve for [tex]$x$[/tex]. Subtract 2.1 from both sides:
[tex]$$2x = 7.5 - 2.1.$$[/tex]
Calculating the right side,
[tex]$$7.5 - 2.1 = 5.4,$$[/tex]
so we have
[tex]$$2x = 5.4.$$[/tex]
Dividing both sides by 2 gives
[tex]$$x = \frac{5.4}{2} = 2.7.$$[/tex]
Thus, the equation used and the calculations confirm that the equation is
[tex]$$2.1 + 2x = 7.5.$$[/tex]
Therefore, the correct equation is option 4.
