Question

Mr. Jones is opening a restaurant. A town ordinance states that his

Answer 1

Answer:

(l  = 2 ft, b = 48 ft ), (l  = 4 ft, b = 24 ft ), (l  = 8 ft, b = 12 ft ), (l = 16  ft, b = 6)  (l = 32 ft, b = 3 ft ) are the set of possible length and breadth dimension for sign board.

Step-by-step explanation:

Let us assume the possible length of the sign board  =  a ft

And the possible width of the sign board = b ft

The maximum possible area covered by board  = 96 sq ft.

Now,as we know, AREA OF A RECTANGLE  = LENGTH x WIDTH

So, here:

Area of sign board = Possible ( length x Width) of board

⇒ 96 sq ft  =    a x b      .......... (1)

Now, by prime factorization, 96 = 2 x 2 x 2 x 2 x 2 x 3

Now, also, 96  =  2 x 48     ⇒  a  = 2 ft, b = 48 ft

                         = 4 x 24     ⇒  a  = 4 ft, b = 24 ft

                         = 8 x 12      ⇒  a  = 8 ft, b = 12 ft

                         = 16 x  6      ⇒  a  = 16  ft, b = 6  ft

                         = 32 x  3     ⇒  a  = 32 ft, b = 3 ft

As, all above mentioned values of a and b  gives the area  = 96 sq ft

Hence, these are the given possible dimensions of the sign board