We are tasked with finding:

a) The upper bound for the area of the rectangle.
b) The lower bound for the perimeter of the rectangle.

The lengths of the rectangle are given as:

• Length: 43.4 cm
• Width: 24.8 cm

Step 1: Understanding bounds for measurements

Since the lengths are measured to the nearest tenth of a centimeter, we have to consider the bounds for each dimension.

• Upper bound for length: $43.4 + 0.05 = 43.45$ cm

• Lower bound for length: $43.4 - 0.05 = 43.35$ cm

• Upper bound for width: $24.8 + 0.05 = 24.85$ cm

• Lower bound for width: $24.8 - 0.05 = 24.75$ cm

Step 2: Calculation

a) Upper bound for the area

The area of a rectangle is given by: $\text{Area} = \text{Length} \times \text{Width}$ To get the upper bound, we use the upper bound of the length and width: $\text{Upper bound for area} = 43.45 \times 24.85$

b) Lower bound for the perimeter

The perimeter of a rectangle is given by: $\text{Perimeter} = 2(\text{Length} + \text{Width})$ To get the lower bound, we use the lower bound of the length and width: $\text{Lower bound for perimeter} = 2(43.35 + 24.75)$

Let me calculate the values.The results are:

a) The upper bound for the area of the rectangle is approximately 1079.73 cm².

b) The lower bound for the perimeter of the rectangle is 136.2 cm.

Do you need more details or have any questions?

Here are five related questions to explore further:

1. How would the upper bound for the perimeter be calculated?
2. What would the lower bound for the area of the rectangle be?
3. Can these bounds affect real-world measurements, and how?
4. How does rounding affect the accuracy of calculations?
5. Can you calculate the perimeter using only the upper bounds?

Tip: When measuring, always account for potential errors in rounding to get the most accurate estimate.