Let's break down the problem step by step.
1. Total Perimeter and Longest Side:
- Given perimeter of the triangle is [tex]\( 14.5 \)[/tex] cm.
- The longest side measures [tex]\( 6.2 \)[/tex] cm.
2. Relation between Longest Side and Shortest Side:
- The longest side is twice the shortest side.
- Let's denote the shortest side by [tex]\( a \)[/tex]. Thus, [tex]\( 2a = 6.2 \)[/tex] cm.
3. Calculating the Shortest Side:
[tex]\[
2a = 6.2 \implies a = \frac{6.2}{2} = 3.1 \text{ cm}
\][/tex]
4. Summation of the Sides:
- Since the perimeter is the sum of all the sides, let the middle side be [tex]\( b \)[/tex].
- We can set up the equation for the perimeter:
[tex]\[
a + b + \text{longest side} = 14.5
\][/tex]
- Substituting the known values:
[tex]\[
3.1 + b + 6.2 = 14.5
\][/tex]
5. Solving for the Middle Side ([tex]\(b\)[/tex]):
[tex]\[
3.1 + 6.2 + b = 14.5 \implies 9.3 + b = 14.5
\][/tex]
[tex]\[
b = 14.5 - 9.3 = 5.2 \text{ cm}
\][/tex]
6. Verification of the Equation:
- The equation is [tex]\( 9.3 + b = 14.5 \)[/tex].
Therefore, the correct equation that can be used to find the side lengths is:
[tex]\[
9.3 + b = 14.5
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{9.3+b=14.5}
\][/tex]
