Answer:
The width of the walkway is 4 feet.
Step-by-step explanation:
The garden and a walkway around its perimeter have an area of 460 square feet.
The length of the garden = 15 feet
The width of the garden = 12 feet
Assuming that walkway is of uniform width, we can solve the following equation.
[tex](12+2x)\times(15+2x)= 460[/tex]
Expanding this we get;
[tex]4x^{2}+54x+180=460[/tex]
[tex]=> 4x^{2}+54x-280=0[/tex]
We will solve this using quadratic equation formula:
[tex]x=\frac{-b\pm \sqrt{b^{2} -4ac} }{2a}[/tex]
Here a = 4 , b = 54 , c = -280
We get the roots as x = 4 and x = [tex]-\frac{35}{2}[/tex]
Neglecting the negative value, we will take x = 4 feet.
Hence, the width of the walkway is 4 feet.
