The side length of the following square can be expressed by the equation ℓ=A−−√, where A represents the area of the square.
What is the side length of the square if the area is 4x+12 in.2?
6 inches
−6 inches
2 inches
−2 inches
well, the side length must be positive, so that eliminates B and D
To find the side length of the square, we need to substitute A = 4x + 12 into the equation ℓ = A−−√.
Thus,
ℓ = 4x + 12−−√
Simplifying this equation, we have:
ℓ = (√(4x + 12))
Now, to determine the side length of the square when the area is 4x + 12 in.2, we need to substitute x into the equation.
Since the equation is a square root, we need to solve for the value of (√(4x + 12)).
When x = 0, the side length of the square is:
ℓ = (√(4(0) + 12))
ℓ = (√(12))
ℓ = √(4 × 3)
ℓ = 2√3
Therefore, the side length of the square is 2√3 inches.
To find the side length of the square, we need to substitute the given area into the equation ℓ = √A.
Given that A = 4x + 12 in^2, we can substitute this into the equation and solve for the side length (ℓ):
ℓ = √(4x + 12)
Now let's substitute A with the given value (4x + 12):
ℓ = √(4x + 12)
ℓ = √(4(x + 3))
Now we can simplify the expression inside the square root:
ℓ = √(4(x + 3))
ℓ = √(4x + 12)
ℓ = √4 * √(x + 3)
ℓ = 2 * √(x + 3)
So the side length of the square is 2√(x + 3).
Note: The answer cannot be determined without knowing the value of x. Therefore, we cannot determine whether the side length is 6 inches, -6 inches, 2 inches, or -2 inches without further information.