sam decides to build a square garden if the area of the other garden is 9x^2 -24x +16 square feet what is the length of one side of the garden
√(9x^2 -24x +16) = 3x - 4
To find the length of one side of the square garden, we can use the formula for the area of a square.
The area of a square can be found by squaring the length of one side, so we need to take the square root of the given area to find the length of one side.
Let's calculate it step by step:
1. Start with the given area: 9x^2 - 24x + 16 square feet.
2. Take the square root of the area to find the length of one side:
√(9x^2 - 24x + 16)
3. Simplify the expression under the square root:
√[(3x - 4)(3x - 4)]
4. Apply the square root property and simplify further:
(3x - 4)
Therefore, the length of one side of the square garden is 3x - 4.
To find the length of one side of the garden, we need to determine the square root of the area. In this case, the area of the garden is given by the quadratic expression 9x^2 - 24x + 16 square feet.
Step 1: Set up the quadratic equation:
Start by setting the expression for the area equal to a general quadratic equation,
9x^2 - 24x + 16 = A
Step 2: Simplify the equation:
Rearrange the equation to make one side equal to zero,
9x^2 - 24x + (16 - A) = 0
Step 3: Find the roots of the equation:
Apply the quadratic formula to solve for x. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing this formula with the equation 9x^2 - 24x + (16 - A) = 0, we have:
a = 9, b = -24, c = (16 - A)
Plug in these values into the quadratic formula and solve the equation.
Step 4: Calculate the square root of A:
Once you obtain the value(s) for x, substitute it back into the equation for A to get the area in terms of x. Then, calculate the square root of A.
√A = √(9x^2 - 24x + 16)
Hence, the length of one side of the garden will be √A (the square root of the area).