Question

a rectangular sign has a length of 3 and 1/2 ft and width of 1 and 1/8 ft will the area of the sign be greater or less than 3 and 1/2 ft, how do you know? What is the area of the sign?

Answer 1

The area is 3.9375 cubic ft, so yes, the area will greater than 3 and 1/2 ft.

Hope this helps:)

Explanation:

Answer 2

Length of a rectangular sign :-

`= 3 (1)/(2) \: \: m`

Width of a rectangular sign :-

`= 1 (1)/(8) \: \: m`

We know that :-

The formula for finding the area of a rectangle is :-

`=\bold{ length * breadth}`

Which means :-

The area of the rectangular sign:-

`=3 (1)/(2) * 1 (1)/(8)`

`= ((2 * 3 )+ 1)/(2) * ((8 * 1) + 1)/(8)`

`= (6 + 1)/(2) * (8 + 1)/(8)`

`= (7)/(2) * (9)/(8)`

`= (7 * 9)/(2 * 8)`

`= (63)/(16)`

`={3 (15)/(6) \: \: }`

`= 3 (15 / 3)/(6 / 3)`

`={ 3 (5)/(2) \: m}`

Thus, the area of the rectangular sign is:-

`=\bold{ 3 (5)/(2) \: m}`

We can see that :-

`\bold{3 (5)/(2) \: > 3 \: (1)/(2) \: }`

Which will mean that the area of the rectangular sign is greater than
`{ 3 (1)/(2) \: m}`.

Therefore, the area of the rectangular sign is =
`\bold{ 3 (5)/(2) \: m}` and it is greater than
`\bold{ 3 (1)/(2) \: m}` .