Question

a rectangular pool is 41.9 feet long and 19.6 feet wide. what is the best estimate for the area of the pool?
200 ft²
300 ft²
600 ft²
800 ft²
1000 ft²

Explanation:

Step1: Recall area of rectangle formula

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \).

Step2: Estimate length and width

Estimate \( 41.9 \) as \( 40 \) (since \( 41.9 \) is close to \( 40 \)) and \( 19.6 \) as \( 20 \) (since \( 19.6 \) is close to \( 20 \)).

Step3: Calculate estimated area

Using the estimated values, \( A \approx 40 \times 20 = 800 \, \text{ft}^2 \)? Wait, no, wait. Wait, \( 41.9 \) is closer to \( 40 \) or \( 42 \)? Wait, but for estimation, maybe round \( 41.9 \) to \( 40 \) and \( 19.6 \) to \( 20 \), but \( 40\times20 = 800 \), but wait, \( 41.9\times19.6 \approx 42\times20 = 840 \), but the options are 200, 300, 600, 800, 1000. Wait, maybe another way: \( 41.9 \approx 40 \), \( 19.6 \approx 20 \), \( 40\times20 = 800 \), but wait, \( 41.9\times19.6 = (40 + 1.9)(20 - 0.4)= 40\times20 - 40\times0.4 + 1.9\times20 - 1.9\times0.4 = 800 - 16 + 38 - 0.76 = 800 + 22 - 0.76 = 821.24 \), which is close to 800. Wait, but let's check the options. The options are 200, 300, 600, 800, 1000. So the best estimate is 800? Wait, no, wait, maybe I made a mistake. Wait, \( 41.9 \) is about 40, \( 19.6 \) is about 20, 4020=800. So the best estimate is 800. Wait, but let's see: 41.919.6. Let's calculate 4020=800, 4220=840, 4019=760. So 41.919.6 is between 760 and 840, and 800 is in that range. So the best estimate is 800.

Answer:

800 ft² (corresponding to the option with 800 ft²)