https://file.aiquickdraw.com/mathbot/file/1727195336586c8hwc4h6.jpg

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.

The lengths of the rectangle have been measured to the nearest tenth of a centimeter. Work out the following: a) The upper bound for the area of the rectangle. b) The lower bound for the perimeter of the rectangle.

Solve a problem involving bounds for the area and perimeter of a rectangle with lengths measured to the nearest tenth of a centimeter. Learn how to find the upper bound for the area and lower bound for the perimeter with key geometric formulas.

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