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]\( 4.2 + y = 7.5 \)[/tex]
C. [tex]\( y - 4.2 = 7.5 \)[/tex]
D. [tex]\( 2.1 + 2x = 7.5 \)[/tex]



Answer :

Let's solve the problem step by step:

1. We know the triangle is isosceles, which means it has two sides of equal length, and let's denote these equal sides as [tex]\( x \)[/tex]. The shortest side is given as [tex]\( y \)[/tex], and it measures 2.1 meters.

2. We are also given that the perimeter of the triangle is 7.5 meters. The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, in this case, the perimeter can be written as:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
Simplifying this, we get:
[tex]\[ \text{Perimeter} = 2x + y \][/tex]

3. Substituting the given values into the perimeter expression:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]

4. Thus, to find the equation that can be used to determine the value of [tex]\( x \)[/tex], we rearrange the perimeter expression to the standard form:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]

Therefore, the equation that can be used to find the value of [tex]\( x \)[/tex] given that the shortest side [tex]\( y \)[/tex] measures 2.1 meters is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]