2) The area of the assembly area is:
A = 124m x 92m = 11368m²
Each student occupies an area of 1m x 1m = 1m². Therefore, the total area occupied by the students is:
A_student = number of students x 1m²
To find the area that is not occupied by the students, we need to subtract A_student from the total area of the assembly area:
A_not_occupied = A - A_student
We can find the number of students by dividing the area of the assembly area by the area per student:
number of students = A / A_student = 11368m² / 1m² = 11368
Therefore, the area not occupied by the students is:
A_not_occupied = A - A_student = 11368m² - 11368 = 10000m²
Answer: The area not occupied by the students is 10000m².
The answer is not one of the given options.
3) Let the existing number of students be n. If 69 students are removed, the new number of students is:
n - 69
For the smallest number that must be divided to get a perfect square, we need to find the prime factorization of n - 69 and identify the factors that are not in pairs. These factors need to be multiplied to get the smallest number that must be divided to get a perfect square.
For example, if n - 69 = 300, the prime factorization of 300 is:
300 = 2² x 3 x 5²
The factors that are not in pairs are 3 and 2. Therefore, the smallest number that must be divided to get a perfect square is:
2 x 3 = 6
Answer: The smallest number that must be divided to get a perfect square depends on the value of n, which is not given in the question.
4) Let the number of students in each row be r. If 5 rows and 5 columns are added, the new number of students is:
(r + 5) x (r + 5)
The original number of students is:
r x (r + 5)
We can set these two expressions equal to each other and solve for r:
r x (r + 5) = (r + 5) x (r + 5)
r² + 5r = r² + 10r + 25
5r = 25
r = 5
Therefore, the number of students in each row is:
r = 5
Answer: The formula for the number of students in each row after 5 rows and 5 columns are added is r + 5, where r is the original number of students in each row.