A rectangular grass area ub a park measures 50 yards by 100 yards. The city wishes to put a uniform sidewalk around the grass area which would increase the area by 459 yd ^2. What is the width of sidewalk
Is it 9.18 feet
I mean yards
Follow my steps in your previous post
http://www.jiskha.com/display.cgi?id=1459994336
To find the width of the sidewalk, we need to calculate the increase in area and then divide it by the width of the sidewalk.
1. Calculate the original area of the grass area:
Area = Length × Width
Area = 50 yards × 100 yards
Area = 5000 yd^2
2. Calculate the increased area:
Increased Area = Original Area + Area Increase
Increased Area = 5000 yd^2 + 459 yd^2
Increased Area = 5459 yd^2
3. Let's assume the width of the sidewalk is "w" yards. This means that the new dimensions of the grass area including the sidewalk would be:
Length = 50 yards + 2w
Width = 100 yards + 2w
4. Calculate the new area of the grass area including the sidewalk:
New Area = Length × Width
New Area = (50 + 2w) yards × (100 + 2w) yards
5. Set up an equation using the increased area:
New Area - Original Area = 5459 yd^2
(50 + 2w) × (100 + 2w) - 5000 = 5459
6. Simplify the equation:
5000 + 100w + 2w^2 + 200w + 4w^2 - 5000 = 5459
6w^2 + 300w - 459 = 0
7. Use the quadratic formula to solve for "w":
w = (-b ± √(b^2 - 4ac)) / (2a)
where a = 6, b = 300, and c = -459
w = (-300 ± √(300^2 - 4(6)(-459))) / (2(6))
w = (-300 ± √(90000 + 11016)) / 12
w = (-300 ± √101016) / 12
8. Calculate the values of "w":
w ≈ (-300 + √101016) / 12 ≈ 8.09
w ≈ (-300 - √101016) / 12 ≈ -58.24 (ignore this value since we cannot have a negative width)
Hence, the width of the sidewalk is approximately 8.09 yards. To convert this to feet, we can multiply by 3 since there are 3 feet in a yard:
Width in feet ≈ 8.09 yards × 3 feet/yard ≈ 24.27 feet
Therefore, the width of the sidewalk is approximately 24.27 feet, not 9.18 feet.