Quadratic equations

Question

a rectangle has lenght 4 cm greater than it's width. Find it's width given that it's area is 96cm²

Answer 1

Let x = the width of the rectangle

The length is then x+4.

 

The area of the rectangle is equal to length * width.  Therefore, the area is x*(x+4)

 

x*(x+4) = 96

 

x² + 4x = 96    (distribute the x)

 

x² + 4x - 96 = 0   (subtract 96 from both sides)

 

Factor:

 

(x+12)(x-8) = 0

 

(x+12) = 0   or (x-8) = 0

Therefore, x = -12 or x = 8

 

The rectangle can't have negative length, so the width is equal to 8.