Final answer:
Without additional information, the exact length and width of Ciara's garden cannot be determined from the area expression (3x²+4x) square feet. This is because there are infinitely many pairs of factors that could yield this product.
Step-by-step explanation:
Ciara has a garden with a total area of (3x²+4x) square feet. To determine the length and width of the garden, one would usually factor this expression, assuming it represents the product of the length and width of a rectangle. However, this expression is not easily factorable into two binomials with integer coefficients, so we might need more information to give an exact answer for length and width.
In the case of a perfect square trinomial or a rectangle where one side is a linear binomial and the other is a constant, we could say the garden's dimensions are those factors. However, without additional information or constraints, there are infinitely many possible combinations of length and width that could give us this area since any two expressions that multiply to (3x²+4x) would work.
A helpful trick in dealing with area is to remember that the area of a rectangle is found by multiplying length by width (Area = Length × Width), so the units of area should be square units (like square feet in this case). If we had one dimension, we could solve for the other by dividing the area by the known dimension.