Question

The length of a wall is 12m more than its width. If the area of the wall is less than 64m^(2) which of the following could be its length? A. 3m B. 4m C. 15m D. 16m

Answer 1

Width = x

Length = x + 12

Area:

(x+12)x < 64

`x^(2) +12x < 64`

`x^(2) +12x - 64 < 0`

Δ
`= 12^(2) - 4 * 1 * (-64) = 144 + 256 = 400`

`x_(1) = (12 - 20)/(2) = -4`

`x_(2) = (12+20)/(2) = 16`

x⊆(-4, 16)

X can't be negative because length and width can't be negative numbers.

Answer D is wrong because X needs to be less than 16.

Answers A, B, C are correct