Question

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?
(3x + 4) feet

(3x − 4) feet

(4x − 3) feet

(4x + 3) feet ...?

Answer 1

(3x − 4) feet

Solve as a square:
(3x - 4)(3x - 4) = 9x² − 24x + 16

Answer 2

Answer:  The correct option is (B) $(3x-4).$

Step-by-step explanation:  Given that Sam decides to build a square garden whose area is as follows:

$A=9x^2-24x+16~\textup{square feet}.$

We are to find the length of one side of the garden.

Since the given garden is of a square shape, so the length of each side is same.

That is, the area of the garden must be a perfect square trinomial.

We have

$A\\\\=9x^2-24x+16\\\\=(3x)^2-2\times 3x\times 4+4^2\\\\=(3x-4)^2.$

Since the area of a square is (length)², so the length of one side of the garden is $(3x-4)~\textup{feet}.$

Thus, (B) is the correct option.