According to health and safety policy, classrooms should allow for 1.8sqm of floor space per person and an additional 9sqm.

A plan indicates that a classroom's floor dimensions should be 12.0m by 4.5m
a Based on these figures, clculate the maximum number of students that can use the classroom, assuming there is only one teacher present.
b If the dimensions have been corrected to 1 dp calculate the maximum and minimum possible floor areas
c investigate the absolute and relative errors between the minimum possible floor area and the plan's floor area, and the significance in terms of potential number of students in the classroom.

The floor area is 12 x 4.5 = 54 m^2
Let N be the number of students. The minimum area required for N students is
A = 1.8 (N+1)+ 9
if A = 54,
N+1 = 45/1.8 = 25
N = 24 students (and 1 teacher)

a) To calculate the maximum number of students that can use the classroom, we need to divide the total floor area by the minimum floor area required per person.

Given:
Floor dimensions: 12.0m by 4.5m
Floor area: 12.0m * 4.5m = 54.0sqm
Minimum floor area per person: 1.8sqm
Additional floor area: 9.0sqm

To calculate the maximum number of students:
Total floor area = Minimum floor area per person * (Number of students + 1) + Additional floor area

54.0sqm = 1.8sqm * (N + 1) + 9.0sqm

Subtracting 9.0sqm from both sides:
45.0sqm = 1.8sqm * (N + 1)

Dividing both sides by 1.8sqm:
25.0 = N + 1

Subtracting 1 from both sides:
N = 24

Therefore, the maximum number of students that can use the classroom, assuming there is only one teacher present, is 24.

b) If the dimensions have been corrected to 1 decimal place, we need to calculate the maximum and minimum possible floor areas:

Maximum floor area:
Floor dimensions: 12.0m by 4.5m (uncorrected)
Maximum floor area = 12.0m * 4.5m = 54.0sqm

Minimum floor area:
Floor dimensions (corrected to 1 decimal place):
Length = 12.0m (corrected to 1 decimal place) = 12.0m
Width = 4.5m (corrected to 1 decimal place) = 4.5m

Minimum floor area = 12.0m * 4.5m = 54.0sqm

c) To investigate the absolute and relative errors between the minimum possible floor area and the plan's floor area, and their significance in terms of potential number of students in the classroom, we need to compare the two values.

Absolute error:
Absolute error = |Plan's floor area - Minimum possible floor area|
= |54.0sqm - 54.0sqm|
= 0sqm

Relative error:
Relative error = Absolute error / Plan's floor area * 100
= 0sqm / 54.0sqm * 100
= 0%

The absolute error and relative error between the minimum possible floor area and the plan's floor area are both 0. This means that the minimum possible floor area and the plan's floor area are identical.

Since there is no error, there is no impact on the potential number of students in the classroom. The maximum number of students that can use the classroom remains 24, as calculated previously.