Answer :
Sure, let's solve the problem step by step:
We know the following:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side of the triangle measures 2.1 meters.
An isosceles triangle has two sides that are equal in length, and let's call the length of these equal sides [tex]\(x\)[/tex].
The formula for the perimeter of a triangle is:
[tex]\[ \text{Perimeter} = \text{side 1} + \text{side 2} + \text{side 3} \][/tex]
For our isosceles triangle, this formula becomes:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We are given:
- The perimeter is 7.5 meters.
- The shortest side [tex]\(y\)[/tex] is 2.1 meters.
Substitute the given values into the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
To isolate [tex]\(x\)[/tex], we need to solve for [tex]\(x\)[/tex]. We can do this by subtracting 2.1 from both sides of the equation:
[tex]\[ 7.5 - 2.1 = 2x \][/tex]
[tex]\[ 5.4 = 2x \][/tex]
Now, we need to isolate [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{5.4}{2} \][/tex]
Thus, the correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
From this equation, solving for [tex]\(x\)[/tex] would give the sides of the triangle. But the initial equation we started with, which is correct, is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct equation from the given options is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Thus, the correct choice from the provided options is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]
We know the following:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side of the triangle measures 2.1 meters.
An isosceles triangle has two sides that are equal in length, and let's call the length of these equal sides [tex]\(x\)[/tex].
The formula for the perimeter of a triangle is:
[tex]\[ \text{Perimeter} = \text{side 1} + \text{side 2} + \text{side 3} \][/tex]
For our isosceles triangle, this formula becomes:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
[tex]\[ \text{Perimeter} = 2x + y \][/tex]
We are given:
- The perimeter is 7.5 meters.
- The shortest side [tex]\(y\)[/tex] is 2.1 meters.
Substitute the given values into the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
To isolate [tex]\(x\)[/tex], we need to solve for [tex]\(x\)[/tex]. We can do this by subtracting 2.1 from both sides of the equation:
[tex]\[ 7.5 - 2.1 = 2x \][/tex]
[tex]\[ 5.4 = 2x \][/tex]
Now, we need to isolate [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{5.4}{2} \][/tex]
Thus, the correct equation to find the value of [tex]\(x\)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
From this equation, solving for [tex]\(x\)[/tex] would give the sides of the triangle. But the initial equation we started with, which is correct, is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct equation from the given options is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Thus, the correct choice from the provided options is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]
