Question

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

Answer 1

Start with the basic formulas for perimeter and area: 1) P = 2(L+W) where L = Length and W = Width. 2) A = L*W You are given that P = 300m and A = 5000 sq.m. so plug these values into the two equations thus: 1a) 300 = 2(L+W) 2a) 5000 = L*W Now you have a system of equations with two unknowns. Solve equation 1a) for L 1b) L = 150-W now substitute this into equation 2a) and solve for W. 2b) 5000 = (150-W)*W Simplify this. W^2-150W+5000 = 0 This quadratic equation can be solved by factoring, so... (W-100)(W-50) = 0 So W = 100 or W = 50 Now 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