Answer :
To find the equation that can be used to determine the value of [tex]\( x \)[/tex], let's first understand the problem.
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length, and the third side can be different. We know that the shortest side, [tex]\( y \)[/tex], is 2.1 meters. Typically, in an isosceles triangle, the two equal sides are longer than the base (the shortest side), but it is possible for the equal sides to be the shortest side in some cases.
Let's assume [tex]\( x \)[/tex] represents the length of the two equal sides of the triangle. The formula for the perimeter of a triangle is the sum of all its sides.
So, the expression for the perimeter is:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Simplifying gives:
[tex]\[ 2x + y = 7.5 \][/tex]
Now we substitute the known value of [tex]\( y \)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This equation matches one of the options provided:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the correct equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
We have an isosceles triangle with a perimeter of 7.5 meters. In an isosceles triangle, two sides are of equal length, and the third side can be different. We know that the shortest side, [tex]\( y \)[/tex], is 2.1 meters. Typically, in an isosceles triangle, the two equal sides are longer than the base (the shortest side), but it is possible for the equal sides to be the shortest side in some cases.
Let's assume [tex]\( x \)[/tex] represents the length of the two equal sides of the triangle. The formula for the perimeter of a triangle is the sum of all its sides.
So, the expression for the perimeter is:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Simplifying gives:
[tex]\[ 2x + y = 7.5 \][/tex]
Now we substitute the known value of [tex]\( y \)[/tex]:
[tex]\[ 2x + 2.1 = 7.5 \][/tex]
This equation matches one of the options provided:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
So, the correct equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]
