Answer :
To solve this problem, let's break down what's given and what we need to find:
1. We know that we have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length.
2. The shortest side of the triangle, denoted as [tex]\( y \)[/tex], has a length of 2.1 meters.
3. We're asked to find an equation to solve for [tex]\( x \)[/tex], which represents the length of the two equal sides of the triangle.
Let's set up the equation step-by-step:
- The perimeter of the triangle is the sum of all its sides. Since it’s an isosceles triangle, two sides are equal, and we’ll denote each of these sides as [tex]\( x \)[/tex].
- So, the sides can be represented as: two equal sides [tex]\( x \)[/tex], and the shortest side [tex]\( y = 2.1 \)[/tex].
- The equation for the perimeter would be:
[tex]\[
x + x + y = 7.5
\][/tex]
- Substituting the value for [tex]\( y \)[/tex]:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- Simplify the equation by combining like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This derived equation corresponds to the option [tex]\( 2.1 + 2x = 7.5 \)[/tex].
So, the equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] can be used to find the value of [tex]\( x \)[/tex], representing the lengths of the two equal sides in the isosceles triangle.
1. We know that we have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length.
2. The shortest side of the triangle, denoted as [tex]\( y \)[/tex], has a length of 2.1 meters.
3. We're asked to find an equation to solve for [tex]\( x \)[/tex], which represents the length of the two equal sides of the triangle.
Let's set up the equation step-by-step:
- The perimeter of the triangle is the sum of all its sides. Since it’s an isosceles triangle, two sides are equal, and we’ll denote each of these sides as [tex]\( x \)[/tex].
- So, the sides can be represented as: two equal sides [tex]\( x \)[/tex], and the shortest side [tex]\( y = 2.1 \)[/tex].
- The equation for the perimeter would be:
[tex]\[
x + x + y = 7.5
\][/tex]
- Substituting the value for [tex]\( y \)[/tex]:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]
- Simplify the equation by combining like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]
This derived equation corresponds to the option [tex]\( 2.1 + 2x = 7.5 \)[/tex].
So, the equation [tex]\( 2.1 + 2x = 7.5 \)[/tex] can be used to find the value of [tex]\( x \)[/tex], representing the lengths of the two equal sides in the isosceles triangle.
