Question

6 a rectangle has a length that is 2 inches less than 3 times the width, w. which equation describes the area, a, of the rectangle in square inches?
a ( a = 2w^2 - 3w )
b ( a = 3w^2 - 2 )
c ( a = 3w^2 - 2w )
d ( a = 2w^2 - 3 )

Explanation:

Step1: Define length in terms of width

The width is \( w \). The length is 2 inches less than 3 times the width, so length \( l = 3w - 2 \).

Step2: Recall area formula for rectangle

The area \( A \) of a rectangle is \( A = l \times w \).

Step3: Substitute length into area formula

Substitute \( l = 3w - 2 \) into \( A = l \times w \), we get \( A=(3w - 2)\times w = 3w^{2}-2w \).

Answer:

C. \( A = 3w^{2}-2w \)