General Idea:
When we are working with word problems, we need to follow the below steps:
Step 1: Assign variable for the unknown that we need to find.
Step 2: Write a meaningful mathematical equation using the sentence given
Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.
Applying the concept:
Step 1: Let 'x' be the length of longest side of the fence.
Step 2: We need to set up an equation based on the information given.
[tex] Perimeter\; of\; rectangle=\; 2(\; Longest \; side\; +\; Shortest \; side\; ) [/tex]
Substituting 20 for the perimeter of rectangle, x for Longest side and [tex] \frac{7}{2} [/tex] for the shortest side in the above formula, we get the below equation.
[tex] 2(x+\frac{7}{2} )=20 [/tex]
Step 3: Solving the equation.
[tex] 2(x+\frac{7}{2} )=20\\ Distribute \; 2 \; in \; the \; left \; side \; of \; the \; equation\\ \\ 2x+2 \cdot \frac{7}{2} =20\\ Simplify \; in \; the\; left\; side \; of \;the \;equation\\ \\ 2x+7=20\\ Subtract \; 7 \;on\; both \;sides \; of\; the \; equation\\ \\ 2x+7-7=20-7\\ Combine\; like \; terms\\ \\ 2x=13\\ Divide \; by \; 2\;on \; both\; sides\\ \\ \frac{2x}{2} =\frac{13}{2} \\ Simplify \; fraction\;on \; both \; sides\\ \\ x=6.5 [/tex]
Conclusion:
The length of longest side of the fence is 6.5 feet.
