Question

the area of a rectangle is 16 in². the length is 3 times the width plus 2. use w for width. what is the width in inches? equation? enter this equation as a quadratic equation in standard form ax² + bx + c = 0

Explanation:

Step1: Define length in terms of width

Let width be \( w \). Length \( l = 3w + 2 \).

Step2: Use area formula for rectangle

Area of rectangle \( A = l \times w \). Given \( A = 16 \), so \( (3w + 2)w = 16 \).

Step3: Expand and rearrange to standard form

Expand: \( 3w^2 + 2w = 16 \). Subtract 16: \( 3w^2 + 2w - 16 = 0 \).

Answer:

\( 3w^2 + 2w - 16 = 0 \)