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

Answer :

Sure, let's solve the problem step by step:

We know the following:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side of the triangle measures 2.1 meters.

An isosceles triangle has two sides that are equal in length, and let's call the length of these equal sides [tex]\(x\)[/tex].

The formula for the perimeter of a triangle is:
[tex]\[ \text{Perimeter} = \text{side 1} + \text{side 2} + \text{side 3} \][/tex]

For our isosceles triangle, this formula becomes:
[tex]\[ \text{Perimeter} = x + x + y \][/tex]
[tex]\[ \text{Perimeter} = 2x + y \][/tex]

We are given:
- The perimeter is 7.5 meters.
- The shortest side [tex]\(y\)[/tex] is 2.1 meters.

Substitute the given values into the equation:
[tex]\[ 7.5 = 2x + 2.1 \][/tex]

To isolate [tex]\(x\)[/tex], we need to solve for [tex]\(x\)[/tex]. We can do this by subtracting 2.1 from both sides of the equation:
[tex]\[ 7.5 - 2.1 = 2x \][/tex]
[tex]\[ 5.4 = 2x \][/tex]

Now, we need to isolate [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{5.4}{2} \][/tex]

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

From this equation, solving for [tex]\(x\)[/tex] would give the sides of the triangle. But the initial equation we started with, which is correct, is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]

Therefore, the correct equation from the given options is:
[tex]\[ 2.1 + 2x = 7.5 \][/tex]

Thus, the correct choice from the provided options is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]

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Rewritten by : Jeany