Mr. jones is opening a restaurant. a town ordinance states that his
restaurant sign must have an area no greater than 96 square feet.
1. mr. jones wants his restaurant's sign to have the greatest area
allowable. the dimensions of the sign will be whole numbers
greater than 1. what are the possible dimensions of the sign?
explain.

(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                        

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

idk

step-by-step explanation: