Respuesta :
Answer:
3.41 feet
Step-by-step explanation:
Area = Length × Breath
Area of the rectangular lawn = 100 × 50
= 5000 feet²
The sidewalk must occupy an area no more than 10% of the total lawn area.
So, the area of the sidewalk would be not more than = 10% × 5000
= 0.10 × 5000
= 500 feet²
Let the width of the sidewalk = x feet
area of the side walk = (L×W of the long way) + ((L-x)×W of the short way)
(100 × x) + ((50 - x) × x) < 500
100x + (50-x)(x) < 500
-x² + 150x < 500
-x² + 150x = 500
-x² + 150x - 500 = 0
By using quadratic formula
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{(-150)\pm\sqrt{(150)^2-4(-1)(-500)} }{2(-1)}[/tex]
[tex]x=\frac{-150\pm \sqrt{20500} }{-2}[/tex]
[tex]x=75-5\sqrt{205}[/tex] or [tex]x=75+5\sqrt{205}[/tex]
x = 3.41089 ≈ 3.41 feet or x = 146.58
Therefore, width of the sidewalk would be 3.41 feet.
