Question

Use the Pythagorean Theorem and the square root property to solve the following problem.

Express your answer in simplified radical form.

Then find a decimal approximation to the nearest tenth.

A rectangular park is 12 miles long and 4 miles wide. How long is a pedestrian route that runs diagonally across the​ park? In simplified radical​ form, the pedestrian route is 10 miles long.

Answer 1

The length of the diagonal pedestrian route across the park is 4√10 miles in simplified radical form, and its decimal approximation is approximately 12.6 miles when rounded to the nearest tenth.

Step-by-step explanation:

To find the length of the diagonal path across the park, we use the Pythagorean theorem, where a rectangular park with a length of 12 miles (side a) and a width of 4 miles (side b) forms a right-angled triangle with the diagonal path as its hypotenuse (side c).

The theorem states that a² + b² = c². Plugging in our values gives us 12² + 4² = c², which simplifies to 144 + 16 = c², and further to 160 = c². To solve for c, we take the square root of both sides, √160, which can be simplified further to √(16×10) = 4√10. This is the simplified radical form.

To find the decimal approximation, we calculate the square root of 160, which is approximately 12.6 when rounded to the nearest tenth.

Answer 2

12.6 miles.

Step-by-step explanation:

Let L represent the length of the pedestrian.

We have been given that a rectangular park is 12 miles long and 4 miles wide. We are asked to find the length of a pedestrian route that runs diagonally across the​ park.

We will use Pythagoras theorem to find the length of the pedestrian (Hypotenuse).

`L^2=12^2+4^2`

`L^2=144+16`

`L^2=160`

Now, we will take positive square root of both sides:

`L=√(160)`

`L=√(16*10)`

`L=4√(10)`

`L=12.6491106`

Upon rounding to nearest tenth, we will get:

`L\approx 12.6`

Therefore, the length of the pedestrian is approximately 12.6 miles.