Question

jorges teacher asked him to make a poster for his research project. the area of the poster must be 6 square feet. what might be the length and width of the poster?

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \), or \( A = l \times w \). We know that \( A = 6 \) square feet, so we need to find two positive numbers \( l \) and \( w \) such that \( l \times w = 6 \).

Step2: Find factor pairs of 6

We list the positive integer factor pairs of 6:

• If \( l = 6 \) feet, then \( w=\frac{6}{l}=\frac{6}{6} = 1 \) foot (but also non - integer or other positive real number pairs work, for example, if we consider real numbers, if \( l = 3 \) feet, then from \( A=l\times w\), we have \( 6 = 3\times w\), so \( w=\frac{6}{3}=2 \) feet. Another example: if \( l = \sqrt{6}\) feet, then \( w=\sqrt{6}\) feet (a square), but the most common integer pairs are better for a poster. The factor pairs of 6 are (1,6), (2,3), (3,2), (6,1).

Answer:

Some possible lengths and widths are: length = 3 feet and width = 2 feet (or length = 6 feet and width = 1 foot, or length = 2 feet and width = 3 feet, or length = 1 foot and width = 6 feet, or other positive real number pairs whose product is 6, like length=\(\sqrt{6}\) feet and width=\(\sqrt{6}\) feet).