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]x + y - 4.2 = 7.5[/tex]

D. [tex]2.1 + 2x = 7.5[/tex]

Answer :

To find the value of [tex]\( x \)[/tex] for the given isosceles triangle, let's break down the problem step-by-step.

1. Understand the properties of the isosceles triangle: In an isosceles triangle, two sides are of equal length.

2. Identify the given information:
- The perimeter of the triangle is [tex]\( 7.5 \)[/tex] meters.
- The shortest side, denoted as [tex]\( y \)[/tex], measures [tex]\( 2.1 \)[/tex] meters.

3. Set up the equation for the perimeter:
- Since it's an isosceles triangle, let's assume the two equal sides are [tex]\( x \)[/tex].
- The formula for the perimeter, which is the sum of all sides, is:
[tex]\[
x + x + y = 7.5
\][/tex]

4. Substitute the known value:
- Replace [tex]\( y \)[/tex] with [tex]\( 2.1 \)[/tex]:
[tex]\[
x + x + 2.1 = 7.5
\][/tex]

5. Simplify the equation:
- Combine like terms:
[tex]\[
2x + 2.1 = 7.5
\][/tex]

6. Identify the correct equation:
- From the options provided, the equation that matches this is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

This equation will allow you to solve for [tex]\( x \)[/tex] when you need to find its value.

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