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
