Question

A rectangular dog pen is constructed using a barn wall as one side and 60 meters of fencing for the other three sides. What is the maximum area of the dog pen?

Answer 1

Answer:

450 m²

Step-by-step explanation:

Let x = length of rectangle and y = width of the rectangle.

Therefore,

2x + y = 60...............(1)

Making y subject of the formula, we have:

y = 60 - 2x............... (2)

We know area of a rectangle is length * width i.e A = x*y

Let's substitute (60-2x) for y,

A = x * (60-2x)

= 60x - 2(x)²

= -2x² + 60x

$\frac{dA}{dx} = -2x^2 + 60x =$

-4x + 60 = 0

-4x = -60

$x = \frac{-60}{-4} = 15$

Let's substitute 15 for x in equation 2, we have:

y = 60 - 2(15)

= 60 - 30

y = 30

Since x = 15 & y = 30, the area would be:

A = xy

A = 15 * 30

A = 450 m²

The maximum area of the dog pen is 450m²