Questions: What is the approximate length of the path? A. 9 feet B. 43 feet C. 61 feet D. 85 feet

Transcript text: What is the approximate length of the path? A. 9 feet B. 43 feet C. 61 feet D. 85 feet

Solution

Solution Steps

Step 1: Identify the shape of the path

The path is roughly a diagonal line across a rectangular area, forming a right triangle with the length and width of the rectangular area.

Step 2: Use the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the length of the path is the hypotenuse, and the length and width of the rectangular area are the other two sides.

Let \(c\) be the length of the path. We are given the length of the rectangular area as 35 feet and the width as 50 feet. According to the Pythagorean theorem: \(c^2 = a^2 + b^2\) \(c^2 = 35^2 + 50^2\) \(c^2 = 1225 + 2500\) \(c^2 = 3725\)

Step 3: Calculate the length of the path

To find the length of the path \(c\), take the square root of both sides: \(c = \sqrt{3725}\) \(c \approx 61.03\)

Step 4: Choose the closest answer

The approximate length of the path is 61 feet.