Verified answer

Answer:

The answer is 1/2 m

Step-by-step explanation:

1. Draw the 9m by 11m rectangle inside a bigger rectangle with uniform width around it. (Refer to the attached picture for your reference)

2. Use a variable to represent the uniform width of pathway around the smaller rectangle.

Let x - be the width

3. Create an equation using the area of a rectangle

A = L x W

120 = (11 + 2x)(9 + 2x)     multiply the right side of the equation using FOIL

120 = 99 +22x +18x + 4x²       Method

120 - 99 = 40x + 4x²      Simplify and follow the standard form ax²+bx+c =0

21 = 40x + 4x²                 Transpose 21 to the right side of the equation

4x² + 40x - 21 = 0  

4. Using Quadratic Equation, solve for x.

x = -b ±√b² - 4ac       where a = 4, b = 40, c = - 21

           2a

x = - 40 ±√(40)²- 4(4)(- 21)

                2(4)

x = - 40 ± 44

            8

x = - 40 - 44  and x = -40 + 44

            8                           8

x = -84/8       and x = 4/8

x = -10.5 m and x = 1/2 m

5. Since there is no negative value for width, therefore the answer for the width of the pathway is 1/2 m.