We need to convert the given information to meaningful mathematical equation.
Statement: "George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck.", it means
[tex] Perimeter \; of\; the\; rectangle=48\; feet [/tex]
Assuming ' L ' as length of the rectangle & ' W ' as the width of the rectangle, the perimeter of rectangle is given by the below formula.
[tex] Perimeter \; of\; the\; rectangle\; =\; 2(L+W) [/tex]
We know "the deck is 14 feet long", which means...
[tex] L=14 \; feet [/tex]
Substituting 14 for L and 48 for Perimeter of rectangle in the formula above, we can set up and equation in terms of W.
[tex] 2(L+W)=Perimeter \; of\; the\; rectangle\\ 2(14+W)=48\\ Divide \; 2\; on\; both\; sides, \; we\; get...\\ \\ \frac{2(14+W)}{2}=\frac{48}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ 14+W=24\\ Subtracting\; 14\; on\; both\; sides\\ \\ 14+W-14=24-14\\ Combine\; like\; terms\\ \\ W=10 [/tex]
Conclusion:
The width of the deck is 10 Feet
