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The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of [tex]x[/tex] if the shortest side, [tex]y[/tex], measures 2.1 m?

A. [tex]2x - 2.1 = 7.5[/tex]
B. [tex]4.2 + v = 7.5[/tex]
C. [tex]v - 4.2 = 7.5[/tex]
D. [tex]2.1 + 2x = 7.5[/tex]

Answer :

To determine which equation can be used to find the value of [tex]\( x \)[/tex], let's consider the characteristics of the isosceles triangle:

1. Perimeter of the triangle: The perimeter is given as [tex]\( 7.5 \)[/tex] meters.

2. Sides of the isosceles triangle: In an isosceles triangle, two of its sides are of equal length. Since the shortest side is [tex]\( y = 2.1 \)[/tex] meters, the other two sides, which are equal, will be represented by [tex]\( x \)[/tex].

3. Perimeter Equation: The perimeter of a triangle is the sum of the lengths of its sides. So for the given isosceles triangle, the equation is:
[tex]\[
y + 2x = 7.5
\][/tex]
Here, [tex]\( y \)[/tex] is the shortest side ([tex]\( 2.1 \)[/tex] meters), and [tex]\( 2x \)[/tex] represents the sum of the two equal sides.

4. Substituting the known value: Now, substitute [tex]\( y = 2.1 \)[/tex] into the equation:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

This equation matches one of the options provided: [tex]\( 2.1 + 2x = 7.5 \)[/tex].

Therefore, the correct equation to find the value of [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

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