College

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 this step by step!

Given:
- The perimeter of the isosceles triangle is 7.5 meters.
- The shortest side [tex]\( y \)[/tex] measures 2.1 meters.

In an isosceles triangle, two of its sides are equal in length. Let's denote these equal sides as [tex]\( x \)[/tex].

### Step-by-Step Solution:

1. Identify the sides involved:
- Since [tex]\( y \)[/tex] is the shortest side, the other two sides of the isosceles triangle are [tex]\( x \)[/tex] and [tex]\( x \)[/tex].

2. Write the formula for the perimeter of the triangle:
- The perimeter [tex]\( P \)[/tex] of a triangle is the sum of the lengths of its sides.
- Here, [tex]\( P = x + x + y \)[/tex].

3. Substitute the given values into the equation:
- [tex]\( P = 7.5 \)[/tex] meters.
- [tex]\( y = 2.1 \)[/tex] meters.
- So, the equation becomes:
[tex]\[
7.5 = x + x + 2.1
\][/tex]

4. Simplify the equation:
- Combine the [tex]\( x \)[/tex] terms:
[tex]\[
7.5 = 2x + 2.1
\][/tex]

5. Rewrite the simplified equation in a standard form:
- To isolate [tex]\( x \)[/tex], we need to move 2.1 to the other side by subtracting 2.1 from both sides:
[tex]\[
7.5 - 2.1 = 2x
\][/tex]

6. Perform the subtraction:
[tex]\[
5.4 = 2x
\][/tex]

7. Further simplify to solve for [tex]\( x \)[/tex]:
- Divide both sides by 2:
[tex]\[
x = \frac{5.4}{2}
\][/tex]
- This simplifies to:
[tex]\[
x = 2.7
\][/tex]

### Conclusion:
The correct equation that can be used to find the value of [tex]\( x \)[/tex] given the information is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

Therefore, the correct multiple-choice answer is:
[tex]\[ \boxed{2.1 + 2x = 7.5} \][/tex]

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