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 :

To solve this problem, we need to understand that in an isosceles triangle, two sides are of equal length. Let's break down the problem step-by-step:

1. Understand the Problem: We have an isosceles triangle with a perimeter of 7.5 meters. We know the shortest side of the triangle, denoted by [tex]\( y \)[/tex], measures 2.1 meters.

2. Identify the Sides of the Triangle:
- Since this is an isosceles triangle, two sides are equal. We can assume those two equal sides have a length of [tex]\( x \)[/tex].

3. Form the Equation:
- The perimeter of a triangle is the sum of all its sides. Therefore, the equation for the perimeter will be:
[tex]\[
x + x + y = 7.5
\][/tex]
- Simplifying, we get:
[tex]\[
2x + y = 7.5
\][/tex]

4. Substitute the Value of [tex]\( y \)[/tex]:
- We are given [tex]\( y = 2.1 \)[/tex].
- Substitute [tex]\( y \)[/tex] into the equation:
[tex]\[
2x + 2.1 = 7.5
\][/tex]

5. Select the Correct Answer:
- Looking at the given options, the correct equation that can be used to find [tex]\( x \)[/tex] is:
[tex]\[
2.1 + 2x = 7.5
\][/tex]

This matches the option [tex]\( 2.1 + 2x = 7.5 \)[/tex].

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