Answer:
The width of the path is 3 feet.
Step-by-step explanation:
It is given that a rectangular garden has an area of 12 ft by 5 ft.
The area of a rectangle is
[tex]A=length\times width[/tex]
[tex]A=12\times 5[/tex]
[tex]A_1=60[/tex]
Let the width of the path be x.
New length = 12+2x ft
New width = 5+2x ft
Area of garden including gravel is
[tex]A_2=(12+2x)(5+2x)[/tex]
The area of gravel is
[tex]A=A_1-A_2[/tex]
[tex]A=(12+2x)(5+2x)-60[/tex]
It is given that the area of gravel is 138.
[tex]138=(12+2x)(5+2x)-60[/tex]
Rewrite the equation in standard form.
[tex]4 x^2 + 34 x - 138 = 0[/tex]
Factor form of above equation is
[tex]2 (x - 3) (2 x + 23) = 0[/tex]
Using zero product property, we get
[tex]x-3=0\Rightarrow x=3[/tex]
[tex]2x+23=0\Rightarrow x=-\frac{23}{2}[/tex]
Variable x represents the width of path, so the value of x can not be negative.
Therefore the width of the path is 3 feet.
