Question

A homeowner has 60 feet of fencing to enclose a rectangular garden, with the house forming one side of the garden. What length and width are needed to enclose an area of 418 square feet and use all the fencing?

Answer 1

Let:

$$S = 418 \text{ square feet}$$ $$L = 60 \text{ feet}$$ $$H - ? \text{ length}$$ $$W - ? \text{ width}$$

Let's make a system of equations:

$$\left\{ \begin{array}{l} S = W * H \\ L = H + 2W \end{array} \right.$$ $$\left\{ \begin{array}{l} 418 = W * H \\ 60 = H + 2W \end{array} \right.$$

System solutions:

$$\left\{ \begin{array}{l} H = 22 \text{ feet} \\ W = 19 \text{ feet} \end{array} \right.$$

Answer: Length is 22 feet, width is 19 feet.