Given:
Arear of rectangular rug = 48 sq. feet.
The rug is 8 feet longer than it is wide.
To find:
The width of the rug.
Solution:
Let x feet be the width of the rug.
The rug is 8 feet longer than it is wide.
Length of the rug = (x+8) feet
Area of a rectangle is
[tex]Area=Length\times Width[/tex]
Arear of rectangular rug is 48 sq. feet.
[tex]48=(x+8)\times x[/tex]
[tex]48=x^2+8x[/tex]
[tex]0=x^2+8x-48[/tex]
Splitting the middle term, we get
[tex]x^2+12x-4x-48=0[/tex]
[tex]x(x+12)-4(x+12)=0[/tex]
[tex](x+12)(x-4)=0[/tex]
Using zero product property, we get
[tex](x+12)=0\text{ and }(x-4)=0[/tex]
[tex]x=-12\text{ and }x=4[/tex]
Width cannot be negative. So, [tex]x=4[/tex].
Therefore, the width of the rug is 4 feet.
