Find the dimensions of the largest rectangular garden that can be enclosed by 60m of fencing.

Answer 1

Perimetet of rectangle:

P = 2 L + 2 W

In this case:

2 L + 2 W = 60

Divide both sides by 2

L + W = 30

Subtract W to both sides.

L = 30 - W

Area of a rectangle:

A = L • W = ( 30 - W ) • W =

30 W - W² = - W² + 30 W

Graph of this function is parabola opens downward.

Vertex if this parabola is the maximum.

W coordinate of this parabola vertex is:

W = - b / 2 a = - 30 / 2 • ( - 1 ) =

- 30 / - 2 = 15

W = 15 m

L = 30 - W = 30 - 15 = 15

L = 15 m

Answer 2

Remark:

L = length

W = width

A 15 m x 15 m square is the largest rectangle that can be enclosed with 60 m of a fence.