the diagram represents the area of a rectangle as 9x² + 24x + 16 square units. what are the length and width…

the diagram represents the area of a rectangle as 9x² + 24x + 16 square units. what are the length and width of the rectangle in terms of x? both: 3x + 4 units both: 3x + 8 units width: 3x + 4 units; length: 6x + 12 units width: 3x + 8 units; length: 6x + 8 units

the diagram represents the area of a rectangle as 9x² + 24x + 16 square units. what are the length and width of the rectangle in terms of x? both: 3x + 4 units both: 3x + 8 units width: 3x + 4 units; length: 6x + 12 units width: 3x + 8 units; length: 6x + 8 units

Answer

Explanation:

Step1: Factor the area expression

We know that (a^2 + 2ab+b^2=(a + b)^2). For the expression (9x^{2}+24x + 16), where (a = 3x) ((a^2=9x^{2})), (b = 4) ((b^2 = 16)) and (2ab=2\times3x\times4=24x). So (9x^{2}+24x + 16=(3x + 4)^2).

Step2: Recall rectangle - area formula

The area of a rectangle is (A=\text{length}\times\text{width}). Since (A=(3x + 4)^2=(3x + 4)\times(3x + 4)).

Answer:

A. both: (3x + 4) units