Question

An ecology center wants to set up an experimental garden using 300m of fencing to enclose a rectangular area of 5000m^2. Find the dimensions of the garden

Answer 1

P = 2(L+W) where L = Length and W = Width.A = L*WYou are given that P = 300m and A = 5000 sq.m. so plug these values into the two equations thus:300 = 2(L+W)5000 = L*WNow you have a system of equations with two unknowns.Solve equation 1a) for LL = 150-W now substitute this into equation 2a) and solve for W.5000 = (150-W)*W Simplify this.W^2-150W+5000 = 0 This quadratic equation can be solved by factoring, so...(W-100)(W-50) = 0So W = 100 or W = 50Now we need to find L and we can use equation 1b.L = 150 - W and, if W = 50m, then:L = 100m or, if W = 100m, then:L = 50m.The dimensions of the garden are: 100m by 50m