Question

You have 144 feet of fencing to enclose a rectangular region. What is the maximum area? a) 5184 square feet b) 1292 square feet c) 1296 square feet d) 20.736 square feet e) none

Answer 1

Answer: Option 'c' is correct.

Explanation:

Since we have given that

Perimeter of rectangular region = 144 feet

We need to find the maximum area .

As we know that the area will be maximum iff it is a square.

So, perimeter is given by

`2(l+b)=144\\\\l+b=(144)/(2)=72\\\\l+b=72\\\\l+l=72\ (\because\ l=b)\\\\2l=72\\\\l=(72)/(2)=36`

So, the maximum area would be

`Side^2=36^2=1296\ sq.\ feet`

Hence, Option 'c' is correct.