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

Step2: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \), which is \( A = l \times w \).

Step3: Substitute length and area values

We know the area \( A = 48 \) square cm, \( l = w + 2 \), and \( w \) is the width. Substituting into the area formula: \( w(w + 2)=48 \).

Answer:

\( w(w + 2) = 48 \) (the second option: \( w(w + 2) = 48 \))