A factory is to be built on a lot measuring 210 ft by 280 ft. A local building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory.
What must the width of the lawn be?
and If the dimensions of the factory are A ft by B ft with A<B, then A=? B=?
something tells me you did not draw a diagram or do much of anything else. The area of the lot is 58800.
So, if the lawn has width w, the factory has dimensions
(210-2w)(280-2w)
and we know that its area is half of the lot. So,
(210-2w)(280-2w) = 58800/2
Now just solve that for w, and you can then find the desired dimensions
so, draw a diagram, label the dimensions and answer whatever question you have (not shown).
Thanks, those are the same results that I got, but I don't know why it keeps giving me a note that it says that my answer is wrong.
I hope you got w=35. Then the dimensions are 140x210
Check:
140*210 = 29400, half of the lot's area.
To find the width of the lawn, we can start by calculating the area of the factory lot.
The area of a rectangle is found by multiplying its length by its width. In this case, the length is 210 ft and the width is 280 ft. So, the area of the factory lot is:
Area of the factory lot = 210 ft * 280 ft = 58,800 square ft
Since the lawn surrounding the factory has the same area as the factory, we can divide the total area by 2 to get the area of the factory itself:
Area of the factory = 58,800 square ft / 2 = 29,400 square ft
Now, we need to find the dimensions of the factory. Let's assume the width of the lawn is y ft. Since the area of the factory is equal to 29,400 square ft, we can set up the following equation:
(210 ft - 2y) * (280 ft - 2y) = 29,400 square ft
Simplifying the equation, we get:
(210 ft - 2y) * (280 ft - 2y) = 29,400 square ft
58,800 ft^2 - 420y ft - 560y ft + 4y^2 = 29,400 square ft
4y^2 - 980y + 58,800 = 29,400 square ft
Subtracting 29,400 square ft from both sides, we get:
4y^2 - 980y + 29,400 = 0
Now we can solve this quadratic equation to find the width of the lawn. You can use the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = 4, b = -980, and c = 29400. Plugging in these values into the quadratic formula:
y = (-(-980) ± √((-980)^2 - 4*4*29400)) / (2*4)
Calculating further:
y = (980 ± √(960400 + 470400)) / 8
y = (980 ± √(1,430,800)) / 8
y = (980 ± 1196.67) / 8
Dividing both sides by 8:
y = (980 + 1196.67) / 8 or y = (980 - 1196.67) / 8
y ≈ 279.58 ft or y ≈ -34.96 ft
Since we're dealing with dimensions of a lot, a negative value for y doesn't make sense in this context. Therefore, we can disregard the negative solution.
Therefore, the width of the lawn around the factory is approximately 279.58 ft.