Question

You must enclose a rectangular area with 28 m of fencing.

1)What dimensions will give a rectangle with the largest area?

2)What is the maximum area?

Answer 1

A) A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four to find the length of each side. Then find the area by multiplying the length times the width.

B) Approach: For area to be maximum of any rectangle the difference of length and breadth must be minimal. So, in such case the length must be ceil (perimeter / 4) and breadth will be be floor(perimeter /4). Hence the maximum area of a rectangle with given perimeter is equal to ceil(perimeter/4) * floor(perimeter/4).

Answer 2

Answer:

Step-by-step explanation:

p=2l+2w                    

28=2l+2w

28=2l+2w ÷ all by 2

14=l+w

14-w=l

A=lxw

=(14-w)-w

=14-w-w2

=-w2+14w

width= 14÷ 2(-1)

=7m

A=(7)=-(7)2+14(7)

=49m

28=7+7+7+7