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

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* 3x* 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.

Answer 2

(3x − 4) feet

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