Question

cu 3-139. (from lesson 2.3.2)
land is often measured in acres, hectares, or square miles. 1 acre is approximately 0.4 hectares, and 1 square mile is approximately 259 hectares.

a. mike and linda’s yard is 1 hectare. how many acres is it?

b. mike and linda’s neighborhood is 1 square mile. how many acres is it?

Explanation:

Part (a)

Step1: Define the conversion factor

We know that 1 acre ≈ 0.4 hectares. We need to find how many acres are in 1 hectare. Let \( x \) be the number of acres in 1 hectare. We can set up the proportion: \( \frac{1 \text{ acre}}{0.4 \text{ hectares}}=\frac{x \text{ acres}}{1 \text{ hectare}} \)

Step2: Solve for \( x \)

Cross - multiplying gives us \( 0.4x = 1\times1 \). Then, to solve for \( x \), we divide both sides of the equation by 0.4: \( x=\frac{1}{0.4}=\frac{10}{4} = 2.5 \)

Step1: Find the number of hectares in 1 square mile

We know that 1 square mile ≈ 259 hectares.

Step2: Convert hectares to acres

From part (a), we know that to convert hectares to acres, we use the conversion factor \( \frac{1}{0.4} \) acres per hectare. So, for 259 hectares, the number of acres \( y=259\times\frac{1}{0.4} \)

Step3: Calculate the value of \( y \)

\( y = \frac{259}{0.4}=\frac{2590}{4}=647.5 \)

Answer:

2.5 acres

Part (b)