A rectangular hockey field measures 90metres long by 55metres wide The dimensions are measured to the nearest 2metre and 1metre respectively. Calculate the exact maximum percentage error in the perimeter of the field.
To calculate the maximum percentage error in the perimeter of the field, we need to find the maximum possible error in the length and the maximum possible error in the width.
The maximum possible error in the length can be found by subtracting the actual length by the measured length:
Max error in length = 90m - 89m = 1m
The maximum possible error in the width can be found by subtracting the actual width by the measured width:
Max error in width = 55m - 54m = 1m
Now, let's calculate the maximum perimeter (P) of the field by adding the maximum possible errors to the length and width:
Max perimeter = (90m + 1m + 1m) + (55m + 1m + 1m) = 153m
Now, let's calculate the maximum percentage error (E) in the perimeter by subtracting the actual perimeter from the maximum perimeter, dividing it by the actual perimeter, and multiplying by 100:
E = [(153m - 90m - 55m) / (90m + 55m)] * 100 = (8m / 145m) * 100 ≈ 5.5%
Therefore, the exact maximum percentage error in the perimeter of the field is approximately 5.5%.