Find the maxmium area of a rectangular plot of land which can be enclosed by rope of length 60 metres

225 m²

Step-by-step explanation:

If W is the width of the rectangle, and L is the length, then:

60 = 2W + 2L

A = WL

Use the first equation to solve for one of the variables:

30 = W + L

L = 30 - W

Substitute into the second equation:

A = W (30 - W)

A = 30W - W²

This is a parabola, so we can find the vertex using the formula x = - b / (2a).

W = - 30 / (2 * - 1)

W = 15

Or, we can use calculus:

dA/dW = 30 - 2W

0 = 30 - 2W

W = 15

Solving for L:

L = 30 - W

L = 15

So the maximum area is:

A = WL

A = (15) (15)

A = 225