Question

Danica has laid out floor tiles so they form a rectangle with a perimeter of 18 inches. what us the diffrence between the greatest and least possible areas of the rectange?

Answer 1

1 by 8 rectangle... that is a area of 8 square inches.
the greatest is 4 by 5 that is a area of 20 square inches.
The difference is 12

Answer 2

Answer with Step-by-step explanation:

Perimeter of rectangle=18 inches

Let l be the length and b be the breath of the rectangle

Then,  2(l+b)=18 inches

i.e. l+b=9 inches

Area=l×b

All the possible values of l,b and area are:

l(in.)            b(in.)           Area(sq. in.)

1                     8               8

2                    7               14

3                    6               18

4                    5               20

5                    4               20

6                    3               18

7                    2               14

8                    1                 8

Minimum area=8 sq. in. and maximum area=20 sq. in.

Difference=20-8

                =12

Hence,  difference between the greatest and least possible areas of the rectangle is:

12