A rectangular carpet was damaged by a chemical substance - NSC Technical Mathematics - Question 11 - 2021 - Paper 2

Given the ordinates of the undamaged part of the carpet are: p; 12 m; 18 m; 15 m; 11 m; and 7 m, we can find p using the mid-ordinate rule for calculating the average height across the intervals. We already know that the total area is 187,5 m². Denote the total heights we have as: 12, 18, 15, 11, and 7. Let p be the last height. By computing the average, we can sum these heights and set the equation:

$A = \frac{1}{2} \times (p + 12 + 18 + 15 + 11 + 7) imes \text{width}$

Substituting the known value, we can solve for p. Given that the width is the sum of x intervals covered by the known ordinates, we identify that:

Thus, after calculations, we find:

$p = 15 \text{ m}$

To find the minimum time required to repair the damaged area, we first need to determine the damaged area by subtracting the area of the undamaged section from the total area.

Using the mid-ordinate rule:

1. Calculate the average area:

   $A_d = \frac{0.25}{2} \times (p + 12 + 18 + 15 + 11 + 7) \times 10 = \frac{0.25}{2} \times (15 + 12 + 18 + 15 + 11 + 7) \times 10$

   After summing the heights:

   $A_d = 87 m²$

2. Since the total area is 187,5 m², the damaged area is:

   $\text{Damaged Area} = 187.5 - 100.5 = 87 m²$

3. Time to repair:

   Since it takes 0,25 hours to repair 1 m², for the damaged area:

   $\text{Time} = 87 m² \times 0.25 = 21.75 \text{ hours}$

Therefore, the minimum time required to repair the damaged area is 21.75 hours.