Question

The area of a square is defined by A(x)=x^2 −6x+9. What is the length of a side of the square?

a) x−3
b) x+3
c) x−1
d) x+1

Answer 1

The length of a side of the square defined by the area A(x) = x^2 − 6x + 9 is (x - 3), which is represented by option a).

Step-by-step explanation:

The area of a square is given by the formula A(x) = x^2 − 6x + 9. To find the length of a side of the square, we need to express A(x) as a perfect square since the area of a square is equal to the side length squared.

step by step explanation:

First, we notice that the equation is already a perfect square trinomial. The factors of 9 that can also combine with -6 to form -6x are -3 and -3. Thus, (x - 3)^2 will expand to x^2 - 6x + 9, which is our given area function. Hence, the length of a side of the square is (x - 3), which aligns with option a).