Fence Enough 6D4850

1. **State the problem:** A farmer wants to build a fence around a rectangular pen that is $16$ feet long. The area of the pen is $80$ square feet. We need to determine if $40$ feet of fencing is enough to enclose the pen. 2. **Identify known values:** Length $L = 16$ feet Area $A = 80$ square feet Perimeter $P = ?$ (to check if $40$ feet is enough) 3. **Find the width $W$ of the pen using the area formula:** $$A = L \times W$$ $$80 = 16 \times W$$ Divide both sides by 16: $$\cancel{16} W = \frac{80}{\cancel{16}}$$ $$W = 5$$ feet 4. **Calculate the perimeter $P$ of the rectangle:** $$P = 2(L + W)$$ $$P = 2(16 + 5)$$ $$P = 2(21) = 42$$ feet 5. **Compare the perimeter to the available fencing:** The farmer has $40$ feet of fencing. The required fencing is $42$ feet. 6. **Conclusion:** Since $40 < 42$, $40$ feet of fencing is not enough to fence in the pen. **Final answer:** No, $40$ feet of fencing is not enough because the perimeter of the pen is $42$ feet.