Question

louise bought 80 metres of fencing to make an enclosure for her pet dog .tommy if louise expects a rectangular enclosure what is the largest area it can have ? explain your answer​

Answer 1

Answer:

400 m^2.

Step-by-step explanation:

The largest  area is obtained where the enclosure is a square.

I think that's the right answer because a square is a special form of a rectangle.

So the square would be 20 * 20  = 400 m^2.

Proof:

Let the  sides of the rectangle be x and y m long

The area A = xy.

Also the perimeter  2x + 2y = 80

x + y = 40

y = 40 - x.

So substituting for y in A = xy:-

A = x(40 - x)

A = 40x - x^2

For maximum value of A  we find the derivative and equate it to 0:

derivative A' =  40 - 2x = 0

2x = 40

x = 20.

So y = 40 - x

= 40 - 20

=20  

x and y are the same value so x = y.

Therefore for maximum area the rectangle is a square.