Sam decides to build a square garden. If the area of the garden is 9x2 − 24x + 16 square feet, what is the length of one side of the garden?
To find the length of one side of the garden, we need to find the square root of the area.
The area of the garden is given by the equation 9x^2 - 24x + 16.
To find the square root of this equation, we can factor it:
9x^2 - 24x + 16 = (3x - 4)(3x - 4)
Taking the square root of both sides, we get:
√(9x^2 - 24x + 16) = √((3x - 4)(3x - 4))
√(9x^2 - 24x + 16) = 3x - 4
So, the length of one side of the garden is 3x - 4 feet.
To find the length of one side of the square garden, we need to find the square root of the area.
Given that the area of the garden is 9x^2 - 24x + 16 square feet, we can take the square root of this expression.
√(9x^2 - 24x + 16) = √((3x - 4)(3x - 4))
Since we are looking for the length of one side, we can set this expression equal to 3x - 4.
3x - 4 = √((3x - 4)(3x - 4))
Squaring both sides of the equation:
(3x - 4)^2 = (3x - 4)(3x - 4)
Expanding the equation:
9x^2 - 24x + 16 = 9x^2 - 12x - 12x + 16
Combining like terms and simplifying:
-24x = -24x
This means that for any value of x, the equation holds true.
Therefore, the length of one side of the garden could be any value.