Lisa is having guests over for a game night. She has two tables that are in the shape of rhombuses. The two tables are the same size. She wants to know how many guests she can seat if she pushes her tables together.
The length of one edge of a table is 6 feet. Each person needs 2 feet of space. No person is seated in the corner of a table.
In the picture below, the length of one edge is highlighted and labeled.
How many guests can Lisa fit at this table?
To determine how many guests Lisa can fit at the table, we need to calculate the area of the combined table and then divide it by the space required for each person.
The formula to find the area of a rhombus is: Area = (diagonal1 * diagonal2) / 2
Since the table is in the shape of a rhombus and we know the length of one edge is 6 feet, we can use this information to find the diagonals.
The diagonals of a rhombus intersect at a right angle and bisect each other. So, each diagonal becomes the hypotenuse of a right triangle with legs of half the length of the edge of the table.
Using the Pythagorean theorem: diagonal^2 = leg^2 + leg^2
Since each edge of the table is 6 feet, each leg of the triangle is 6/2 = 3 feet.
diagonal^2 = 3^2 + 3^2 = 9 + 9 = 18
Taking the square root of both sides, we get: diagonal ≈ √18 ≈ 4.24 feet
Now, we can calculate the area of the combined table:
Area = (diagonal1 * diagonal2) / 2
= (4.24 feet * 4.24 feet) / 2
≈ 9 feet^2
Now, we can determine how many guests Lisa can fit at the table by dividing the area of the table by the space required for each person:
Number of guests = Area / Space required per person
= 9 feet^2 / 2 feet^2
= 4.5
Therefore, Lisa can fit approximately 4.5 guests at this table. Since we cannot have a fraction of a person, the maximum number of guests Lisa can fit at this table is 4.