Answer :
Sure! Let's solve this problem step-by-step.
First, we know the perimeter of the isosceles triangle is 7.5 meters.
In an isosceles triangle, two sides are of equal length. Let's denote the length of each of these equal sides as [tex]\( x \)[/tex].
The shortest side is given to be 2.1 meters, which we can call [tex]\( y \)[/tex].
Since the perimeter is the sum of all three sides of the triangle, we have the equation:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Simplifying this, we get:
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We can substitute the given values into this equation. The perimeter is 7.5 meters, and the shortest side [tex]\( y \)[/tex] is 2.1 meters:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
To isolate [tex]\( x \)[/tex], we need to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the correct equation.
So, the fourth option, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the equation you can use to find the value of [tex]\( x \)[/tex].
First, we know the perimeter of the isosceles triangle is 7.5 meters.
In an isosceles triangle, two sides are of equal length. Let's denote the length of each of these equal sides as [tex]\( x \)[/tex].
The shortest side is given to be 2.1 meters, which we can call [tex]\( y \)[/tex].
Since the perimeter is the sum of all three sides of the triangle, we have the equation:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Simplifying this, we get:
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We can substitute the given values into this equation. The perimeter is 7.5 meters, and the shortest side [tex]\( y \)[/tex] is 2.1 meters:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
To isolate [tex]\( x \)[/tex], we need to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
This is the correct equation.
So, the fourth option, [tex]\( 2.1 + 2x = 7.5 \)[/tex], is the equation you can use to find the value of [tex]\( x \)[/tex].
