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?\\(\bigcirc\\) \\(w(w - 2) = 48\\)\\(\bigcirc\\) \\(w(w + 2) = 48\\)\\(\bigcirc\\) \\(2w(w - 2) = 48\\)\\(\bigcirc\\) \\(2w(w + 2) = 48\\)

Explanation:

Step1: Define variables for length and width

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

Step2: Recall the area formula for a rectangle

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

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

We know the area \( A = 48 \) square centimeters (since there are 48 square - centimeter tiles), \( l = w + 2 \), and \( w \) is the width. Substituting these into the area formula, we get \( 48=w\times(w + 2) \), or \( w(w + 2)=48 \).

Answer:

\( \boldsymbol{w(w + 2)=48} \) (corresponding to the option " \( w(w + 2)=48 \)")