In all cases use the following formula for the are of a rectangular shape:
A = lw
Plot A:
The area and height are known, then, solve the formula for the length l:
l = A/w
repace the given values
l = (204 ft²)/(10.2 ft)
I = 20 ft
For the perimeter you have:
P = 2l + 2w = 2(20 ft) + 2(10.2 ft) = 60.4ft
Plot B:
The length and the perimeter are known. For the expression for the perimeter solve for w:
P = 2l + 2w
w = (P - 2l)/2
replace the values of P and l:
w = (57.56 ft - 2(12.78 ft))/2 = 16 ft
Then, replace in the formula for the area:
A = lw = (12.78 ft)(16 ft) = 204.48 ft²
Plot C:
The area and the height are known. Use the formula for A to obtain the length:
l = A/w = 204.49 ft/14.3 ft = 14.3 ft
and for the perimeter:
P = 2w + 2l = 2(14.3 ft) + 2(14.3 ft) = 57.2 ft
Hence, you can conclude:
- The plost with the least amount of fencing is the plot with the lowest perimeter, hence, Plot C requires the least amount of fencing.
- The plot with the greatest area is Plot A.