Use the Pythagorean Theorem and the square root property

Question

Use the Pythagorean Theorem and the square root property to solve the question. 

express your answer in simplified radical form. then find a decimal approximation to the nearest tenth.

 

A rectangular park is 12 miles long and 6 miles wide. how long is a pedestrian route that runs diagonally across the park?

 

simplified radical form?

 

decimal? 

Answer 1

Since we are looking for the diagonal of the rectangle, we are actually looking for the hypotenuse of the the right triangle.

Let a = 12, b = 6, and solve for c using the Pythagorean Theorem

a² + b²  = c²

 

12² + 6² = c² 

 

144 + 36 = c²    

 

180 = c²    Now, take the square root on both sides

 

c = √180 ≈ 13.42