Answer :
To find the correct equation that matches the given conditions for the isosceles triangle, we need to understand the information provided:
1. The perimeter of the isosceles triangle is 7.5 meters.
2. The triangle has two equal sides labeled as [tex]\( x \)[/tex] and the shortest side labeled as [tex]\( y \)[/tex].
3. The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
The formula for the perimeter of a triangle is:
[tex]\[ \text{Perimeter} = x + x + y = 2x + y \][/tex]
Given that the perimeter is 7.5 meters, we can substitute the known value of [tex]\( y \)[/tex] into this equation. Let's rewrite the equation:
[tex]\[ 2x + y = 7.5 \][/tex]
Now, substitute [tex]\( y = 2.1 \)[/tex] into the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
To solve for [tex]\( x \)[/tex], we simply rearrange the equation:
1. Subtract 2.1 from both sides to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
2. Simplify the right side:
[tex]\[ 2x = 5.4 \][/tex]
3. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct choice from the given options is:
- [tex]\( 2.1 + 2x = 7.5 \)[/tex]
This equation properly represents the relationship and checks out with the given information.
1. The perimeter of the isosceles triangle is 7.5 meters.
2. The triangle has two equal sides labeled as [tex]\( x \)[/tex] and the shortest side labeled as [tex]\( y \)[/tex].
3. The shortest side [tex]\( y \)[/tex] measures 2.1 meters.
The formula for the perimeter of a triangle is:
[tex]\[ \text{Perimeter} = x + x + y = 2x + y \][/tex]
Given that the perimeter is 7.5 meters, we can substitute the known value of [tex]\( y \)[/tex] into this equation. Let's rewrite the equation:
[tex]\[ 2x + y = 7.5 \][/tex]
Now, substitute [tex]\( y = 2.1 \)[/tex] into the equation:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
To solve for [tex]\( x \)[/tex], we simply rearrange the equation:
1. Subtract 2.1 from both sides to isolate the terms with [tex]\( x \)[/tex]:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
2. Simplify the right side:
[tex]\[ 2x = 5.4 \][/tex]
3. Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
So, the correct equation that can be used to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
Therefore, the correct choice from the given options is:
- [tex]\( 2.1 + 2x = 7.5 \)[/tex]
This equation properly represents the relationship and checks out with the given information.
