Question

the table you are setting up is an adjustable length square table. you have 12 people, and your mom says that each person needs 2 3/4 feet of space each. how long should each side be?

Explanation:

Step1: Calculate total space needed

There are 12 people. Each person needs \(2\frac{3}{4}\) feet of space. First, convert \(2\frac{3}{4}\) to an improper fraction: \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\) feet.
The total space needed for 12 people is \(12\times\frac{11}{4}\).

$$12\times\frac{11}{4}=\frac{12\times11}{4}= 3\times11 = 33$$

feet.

Step2: Determine the length of each side of the square table

Since it's a square table, the perimeter \(P\) of a square is \(P = 4s\) (where \(s\) is the side - length). We know the perimeter (total space around the table for people) \(P=33\) feet.
From \(P = 4s\), we can solve for \(s\) by \(s=\frac{P}{4}\).

$$s=\frac{33}{4}=8\frac{1}{4}$$

feet.

Answer:

Each side of the square table should be \(8\frac{1}{4}\) feet.