3405.31 – Pumpkin Patch

You are the proud owner of a square pumpkin patch, enclosed by 200 feet of wooden fencing. The patch has area 0.057 acres. Lumberjack O’Lantern is so pleased with your pumpkins that he sends you 700 feet of wooden fencing to build a second square pumpkin patch!

How many acres will your new square pumpkin patch be?

Solution

The original patch's area is $2500 \ft^2$. The new one has area $175 x 175 = 30625 \ft^2$. Set up the proportion: $\dfrac{2500}{0.057} = \dfrac{30625}{x}$. Solve it to see that the new patch has area 0.698 acres, or almost 0.7 acres.