A rancher constructs two rectangular horse pastures that share a side, as shown. The pastures are enclosed by 1050 feet of fencing. Each pasture has an area of 15,000 square feet.
we know that area each pasture=15000 ft² area each pasture=x*y so 15000=x*y-----> equation 1
perimeter two rectangular pastures=1050 ft perimeter two rectangular pastures=2*[2x+y]+y----> 4x+2y+y---> 4x+3y so 1050=4x+3y----> divide by 3----> 1050/3=(4/3)x+y clear variable y y=350-(4/3)x-----> equation 2
the answer part a) y=350-(4/3)x------> it was proved
Part b)Find the possible lengths and widths of each pasture. substitute equation 2 in equation 1 15000=x*y-----> 15000=x*[350-(4/3)x] 15000=350x-(4/3)x²----> multiply by 3----> 45000=1050x-4x² 4x²-1050x+45000=0
using a graph tool----> to resolve the second order equation see the attached figure
the solution is x=53.942 ft x=208.558 ft
15000=x*y-----> y=15000/x
for x=53.94 ft y=278.09 ft
for x=208.56 ft y=71.92 ft
the possible lengths and widths of each pasture are case 1 x=53.94 ft y=278.09 ft
