The area of a rectangle in square units is represented by the expression x^2 + 10x + 16.
Which expressions represent the length and the width of the rectangle in units?
Select TWO correct answers.
A.) (x + 1)
B.) (x + 2)
C.) (x + 4)
D.) (x + 8)
E.) (x + 10)
F.) (x + 16)
The area of a rectangle is given by the product of its length and width.
To find the length and width of the rectangle, we need to factor the given expression x^2 + 10x + 16.
The factors of x^2 are (x)(x).
The factors of 16 are (1)(16) or (2)(8) or (4)(4).
The combination that produces the middle term of 10x is (4)(4).
Therefore, the factors of the expression x^2 + 10x + 16 are (x + 4)(x + 4), which can also be written as (x + 4)^2.
From this, we can determine that the length and width of the rectangle are both (x + 4).
Thus, the correct expressions that represent the length and width of the rectangle are:
C.) (x + 4)
C.) (x + 4)