The space covered by Adrian's new rug and the the value of x will be x² + 12x + 32 and 4 feets respectively.
Initial dimension of living room rug :
Increase in the length and width by x :
- New length = 8 + x
- New weight = 4 + x
Area of new rug = Length × width
- (8+x) × (4+x) = 32+8x+4x+x²
The square feet of floor space covered by the new rug will be :
Value of x if rug has an area of 96 ft² :
x² + 12x + 32 = 96
x² + 12x + 32 - 96 = 0
x² + 12x - 64 = 0
factorize :
x² + 16x - 4x - 64 = 0
x(x + 16) -4(x + 16)
(x + 16) = 0 or (x - 4) = 0
x = - 16 or x = 4
Length can't be nagative ; hence the value of x will be 4
Learn more :https://brainly.com/question/18112348
