Question

What is the width of a rectangular park that has an area of 1.36×10^8 ft^2 and a length of 1.6×10^4 ft?

Answer 1

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

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

We are provided with the area and the length, so we can rearrange the formula to solve for the width:

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

Now, substituting the given values:

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

Now, we will calculate the width:

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

To perform the division, we can separate the coefficients and the powers of 10:

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

Calculating the coefficient:

\[
\frac{1.36}{1.6} = 0.85
\]

Now, calculating the powers of 10:

\[
\frac{10^8}{10^4} = 10^{8-4} = 10^4
\]

Now, combine the results:

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

Now, we can convert \(0.85 \times 10^4\) to standard form:

\[
0.85 \times 10^4 = 8.5 \times 10^3 \ \text{ft}
\]

Thus, the width of the rectangular park is:

\[
\text{Width} = 8.5 \times 10^3 \ \text{ft} \quad \text{or} \quad 8500 \ \text{ft}
\]

The width of the park is \(8500\) ft.