A square flower garden and a sidewalk around the garden have an area of 400 ft2. The sidewalk has a width of 3 ft. What is the length of one side of the flower garden?
the total width is 20ft (400 = 20x20)
6ft of that is sidewalk (on both ends)
the garden is 14x14
is it square?
If so, then s^2 + (s+6)*3*2+2*3*s=400
figure out what s is ... and figure out how I got that equation...
A cactus casts a shadow that is 14 ft 7 inlong a gate nearby casts a shawdow that is 5 ft longestimate the height of the cactus?
To find the length of one side of the flower garden, we need to determine the total area of both the garden and the sidewalk.
Let's assume the length of one side of the flower garden is represented by "x."
The area of the square garden would then be x^2, as all sides of a square are equal.
The garden is surrounded by a sidewalk with a width of 3 ft on each side. So, the length of the garden plus the width of the sidewalk on both sides would be (x + 2*3) ft.
Hence, the total area of the garden and sidewalk can be represented as (x + 2*3)^2.
According to the given information, this area is equal to 400 ft^2.
Setting up the equation, we have:
(x + 6)^2 = 400
To solve this equation for x, we can expand the equation:
x^2 + 12x + 36 = 400
Rearranging the equation:
x^2 + 12x - 364 = 0
Now we can solve this quadratic equation to find the length of one side of the flower garden. We can either factor the equation or use the quadratic formula:
Let's use the quadratic formula:
x = [-12 ± sqrt(12^2 - 4*1*(-364))] / (2*1)
Calculating the square root and simplifying:
x = [-12 ± sqrt(144 + 1456)] / 2
x = [-12 ± sqrt(1600)] / 2
x = [-12 ± 40] / 2
This gives us two possible solutions:
x1 = (-12 + 40) / 2 = 14 ft
x2 = (-12 - 40) / 2 = -26 ft (which is not a valid length for the flower garden)
Therefore, the length of one side of the flower garden is 14 ft.