Let's break down the problem in the image step by step:

Given Data:

Both Charlie and Tommy have rectangular gardens with a length of 9.73 m.

Part (a):

Charlie's garden has a width of 8.52 m, and you are asked to estimate the area by rounding the width and length to 1 significant figure.

• Length of Charlie's garden: 9.73 m (rounded to 1 significant figure = 10 m)
• Width of Charlie's garden: 8.52 m (rounded to 1 significant figure = 9 m)

To find the area, use the formula for the area of a rectangle: $\text{Area} = \text{Length} \times \text{Width}$

Using the rounded values: $\text{Area} \approx 10 \, \text{m} \times 9 \, \text{m} = 90 \, \text{m}^2$

So, the estimated area of Charlie's garden is 90 m².

Part (b):

Tommy's garden has an area of 37.4 m², and you need to estimate the width by rounding the length and area to 1 significant figure.

• Length of Tommy's garden: 9.73 m (rounded to 1 significant figure = 10 m)
• Area of Tommy's garden: 37.4 m² (rounded to 1 significant figure = 40 m²)

To find the width, rearrange the area formula: $\text{Width} = \frac{\text{Area}}{\text{Length}}$

Using the rounded values: $\text{Width} \approx \frac{40 \, \text{m}^2}{10 \, \text{m}} = 4 \, \text{m}$

So, the estimated width of Tommy's garden is 4 m.

Let me know if you need further clarification or details!

Here are five questions to consider next:

1. How would the answers change if we rounded to 2 significant figures instead of 1?
2. What is the exact area of Charlie's garden using unrounded values?
3. What is the exact width of Tommy's garden using unrounded values?
4. How would you estimate the perimeter of Charlie's garden based on rounded values?
5. How does rounding impact the accuracy of these estimates?

Tip: Always be cautious about rounding, especially in real-life applications where precision matters!