Penning the Pony
To make a pen for his new pony, Ted will use an existing fence as one side of the pen. If he has ninety-six meters of fencing, what are the dimensions of the largest rectangular pen he can make?
First, I thought about creating a visual representation of this problem. In order to find the possible lengths for each side you must use a formula to determine those lengths. X + 2Y = 96 or
Instead of using the guess and check method to solve this problem, I decided to use excel and let excel calculate the answer for me. Cell A1 represented the value of X. Cell B1 contained the formula for Y which was, = (96-A1)/2. And cell C1 contained the area, =A1*B1. Once the formulas were complete, I plugged in 1 for X and dragged my cursor. The largest possible area for this pony pen is 1,151.5 square feet. This is possible if X=47 ft and Y=24.5 ft or X=49 ft and Y =23.5 ft. If you would like to see the spreadsheet click here.