Answer :
To solve the problem of finding the equation that represents the relationship between the perimeter of an isosceles triangle and its sides, we follow these steps:
1. Understand the Problem:
- We have an isosceles triangle with a perimeter of 7.5 meters.
- The shortest side, labeled as [tex]\( y \)[/tex], measures 2.1 meters.
- We need to identify the correct equation that includes [tex]\( x \)[/tex], the length of the two equal sides.
2. Concept of an Isosceles Triangle:
- In an isosceles triangle, two sides are equal.
- The perimeter of the triangle is the sum of all its sides.
3. Formulate the Equation:
- The formula for the perimeter [tex]\( P \)[/tex] of an isosceles triangle is:
[tex]\[ P = 2x + y \][/tex]
- Given [tex]\( P = 7.5 \)[/tex] meters and [tex]\( y = 2.1 \)[/tex] meters, we substitute these values into the formula:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
- Simplify:
[tex]\[ 2x = 5.4 \][/tex]
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
5. Choose the Correct Equation:
- From the rearranged form of the original equation, we see that the correct equation is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the equation used to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
1. Understand the Problem:
- We have an isosceles triangle with a perimeter of 7.5 meters.
- The shortest side, labeled as [tex]\( y \)[/tex], measures 2.1 meters.
- We need to identify the correct equation that includes [tex]\( x \)[/tex], the length of the two equal sides.
2. Concept of an Isosceles Triangle:
- In an isosceles triangle, two sides are equal.
- The perimeter of the triangle is the sum of all its sides.
3. Formulate the Equation:
- The formula for the perimeter [tex]\( P \)[/tex] of an isosceles triangle is:
[tex]\[ P = 2x + y \][/tex]
- Given [tex]\( P = 7.5 \)[/tex] meters and [tex]\( y = 2.1 \)[/tex] meters, we substitute these values into the formula:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 7.5 - 2.1 \][/tex]
- Simplify:
[tex]\[ 2x = 5.4 \][/tex]
[tex]\[ x = \frac{5.4}{2} \][/tex]
[tex]\[ x = 2.7 \][/tex]
5. Choose the Correct Equation:
- From the rearranged form of the original equation, we see that the correct equation is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the equation used to find the value of [tex]\( x \)[/tex] is [tex]\( 2.1 + 2x = 7.5 \)[/tex].
