A rectangle has sides of length 6.1cm and 8.1cm correct to 1 decimal place. Find the lower and upper bound for the perimeter of the rectangle
P = 2 L + 2 w
L min 6.05 max 6.14
w min 8.05 max 8.14
To find the lower and upper bound for the perimeter of the rectangle, we need to consider the possible rounding errors in the given measurements.
Given: Length of one side = 6.1 cm
Length of the other side = 8.1 cm
To calculate the lower and upper bounds, we can consider the worst-case scenarios for rounding errors:
1. For the lower bound: We assume that both measurements are rounded down to the nearest whole number. Therefore, we consider the lengths as 6 cm and 8 cm.
Perimeter = 2 × (Length + Width)
= 2 × (6 cm + 8 cm)
= 2 × 14 cm
= 28 cm
So, the lower bound for the perimeter is 28 cm.
2. For the upper bound: We assume that both measurements are rounded up to the nearest whole number. Therefore, we consider the lengths as 7 cm and 9 cm.
Perimeter = 2 × (Length + Width)
= 2 × (7 cm + 9 cm)
= 2 × 16 cm
= 32 cm
So, the upper bound for the perimeter is 32 cm.
Therefore, the lower bound for the perimeter is 28 cm and the upper bound is 32 cm.