Question

john has 48 square centimeter tiles he wants to use to create a mosaic. he wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width. which equation could john solve to find w, the greatest width in centimeters he can use for the mosaic?
○ ( w(w - 2) = 48 )
○ ( w(w + 2) = 48 )
○ ( 2w(w - 2) = 48 )
○ ( 2w(w + 2) = 48 )

Explanation:

Step1: Define variables for length and width

Let the width of the rectangle be \( w \) centimeters. The length is 2 centimeters longer than the width, so length \( l = w + 2 \) centimeters.

Step2: Recall the area formula for a rectangle

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

Step3: Substitute the values of length, width, and area

We know the area \( A = 48 \) square centimeters, \( l = w + 2 \), and \( w \) is the width. Substituting into the area formula, we get \( 48 = w(w + 2) \), which can be rewritten as \( w(w + 2)=48 \).

Answer:

\( w(w + 2) = 48 \) (corresponding to the option: \( w(w + 2) = 48 \))