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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.

Respuesta :

Answer:

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).

[tex]L^2=12^2+4^2[/tex]

[tex]L^2=144+16[/tex]

[tex]L^2=160[/tex]

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

[tex]L=\sqrt{160}[/tex]

[tex]L=\sqrt{16*10}[/tex]

[tex]L=4\sqrt{10}[/tex]

[tex]L=12.6491106[/tex]

Upon rounding to nearest tenth, we will get:

[tex]L\approx 12.6[/tex]

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

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