A rectangular park has an area of 1.36×10^8 ft2. The length of the park is 1.6×10^4 ft. Divide the area by the lheightto find the width of the park. (1 point)

Question

Responses

8.5×103 ft.
8.5 times 10 cubed ft.

8.5×105 ft.
8.5 times 10 superscript 5 baseline ft.

8.5×102 ft.
8.5 times 10 squared ft.

8.5×10^4 ft.

Answer 1

To find the width of the rectangular park, you can use the formula for the area of a rectangle, which is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:

• Area = \(1.36 \times 10^8\) ft²
• Length = \(1.6 \times 10^4\) ft

You can rearrange the formula to solve for width:

\[ \text{Width} = \frac{\text{Area}}{\text{Length}} \]

Now substitute in the values:

\[ \text{Width} = \frac{1.36 \times 10^8 \text{ ft}^2}{1.6 \times 10^4 \text{ ft}} \]

To divide the numbers, you can divide the coefficients and subtract the exponents (since both numbers are in scientific notation):

1. Divide the coefficients: \[ \frac{1.36}{1.6} = 0.85 \]

2. Subtract the exponents: \[ 10^8 / 10^4 = 10^{(8-4)} = 10^4 \]

Now putting it all together:

\[ \text{Width} = 0.85 \times 10^4 \text{ ft} \]

To express \(0.85\) in scientific notation, \(0.85\) can be written as \(8.5 \times 10^{-1}\). Therefore:

\[ \text{Width} = 8.5 \times 10^{-1} \times 10^4 \text{ ft} = 8.5 \times 10^{(4 - 1)} \text{ ft} = 8.5 \times 10^3 \text{ ft} \]

So, the width of the park is:

\[ 8.5 \times 10^3 \text{ ft} \]

Thus, the correct response is:

8.5×10^3 ft.