Respuesta :
Answer:
8
Step-by-step explanation:
If the width of the path is x, then the dimensions of the combined area would be (20 + 2x) × (24 + 2x). Since the combined area is given as 1440, we can equate this with the area of a rectangle with these dimensions.
1440 = (20 + 2x)(24 + 2x)
Expand the brackets
1440 = 480 + 88x + 4x^2
Rearrange the equation, moving the 1440 to the other side so that it is equal to zero
0 = 4x^2 + 88x - 960
Divide by 4 as it is a common factor
0 = x^2 + 22x - 240
Use the quadratic formula
For an equation of the form 0 = ax^2 + bx + c, the quadratic formula is:
[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x = \frac{ - 22 \pm \sqrt{ {22}^{2} - 4 (1)( - 240)} }{2(1)}[/tex]
[tex]x = \frac{ - 22 \pm \sqrt{484 + 960} }{2}[/tex]
[tex]x = \frac{ - 22 \pm \sqrt{1444} }{2}[/tex]
[tex]x = \frac{ - 22 \pm38}{2}[/tex]
[tex]x = - 11 \pm19[/tex]
[tex]x = 8[/tex]
