Question

a school is constructing a rectangular play area against an exterior wall of the school building. it uses 120 feet of fencing material to enclose three sides of the play area.

write an equation to represent a, the area in square feet, as a function of w, the width in feet.
you must use the variables \a\ and \w\ when entering your answers.

Explanation:

Step1: Define variables and fencing length

Let the width be \( w \) (vertical sides) and length be \( l \) (horizontal side, parallel to the wall). The fencing is used for two widths and one length, so \( 2w + l = 120 \). Solve for \( l \): \( l = 120 - 2w \).

Step2: Area formula for rectangle

The area \( A \) of a rectangle is \( A = \text{length} \times \text{width} \). Substitute \( l = 120 - 2w \) and width \( w \) into the formula: \( A = w(120 - 2w) \). Expand to get \( A = -2w^2 + 120w \).

Answer:

\( A = -2w^2 + 120w \)