Problema Solution
Two gardeners are building fences around each of their rectangular 100 square yard gardens. One gardener purchases 62 yards of fencing. The other buys 30 yards. Explain the reason for each gardener purchasing different lengths of fencing even though both gardens are 100 square feet.
Answer provided by our tutors
let
w1 = the width of the first garden, w1>0
l1 = the length of the first garden, l1>0
w2 = the width of the second garden, w2>0
l2 = the length of the second garden, l2>0
One gardener purchases 62 yards of fencing
2(w1 + l1) = 62
w1 + l1 = 31
The other buys 30 yards
2(w2 + l2) = 30
w2 + l2 = 15
oth gardens are 100 square feet means w1*l1 = w2*l2 = 100
w1 = 100/l1 and w2 = 100/l2
For the first garden plug w1 = 100/l1 into w1 + l1 = 31
100/l1 + l1 = 31
by solving we find
l1 = 27.34 yd
click here to see the step by step solution of the equation
w1 = 100/23.34
w1 = 3.66 yd
For the second garden plug w2 = 100/l2 into w2 + l2 = 15
100/l2 + l2 = 15
by solving we find that the equation doesn't have real solutions
click here to see the step by step solution of the equation
That is why it is not possible that the other gardener buys just 30 yards for fencing.