Longest diagonal: 84.85 ft.
To find the longest straight line that can bisect Bob and Alice's backyard, we need to look for the diagonal of the rectangle, as it will be the longest straight line that divides the rectangle into two equal parts.
The area of a rectangle is given by the formula: Area = Length × Width
In this case, the area of Bob and Alice's backyard is 3600 square feet, and we are looking for the diagonal. Let's assume the length of the backyard is "L" and the width is "W."
So, we have the equation: L × W = 3600
Now, we need to find the diagonal, which we can calculate using the Pythagorean theorem, as the diagonal, length (L), and width (W) form a right-angled triangle.
The Pythagorean theorem states: Diagonal^2 = Length^2 + Width^2
Substituting the values: Diagonal^2 = L^2 + W^2
We also know that Alice walks 60 feet to the neighbor's yard, which means the width (W) of the backyard is 60 feet.
Now, let's solve for the length (L) using the area:
L × W = 3600 L × 60 = 3600 L = 3600 / 60 L = 60 feet
Now, we can find the diagonal:
Diagonal^2 = L^2 + W^2 Diagonal^2 = 60^2 + 60^2 Diagonal^2 = 3600 + 3600 Diagonal^2 = 7200
Diagonal = √7200 Diagonal ≈ 84.85 feet
So, the longest straight line that can bisect Bob and Alice's backyard is approximately 84.85 feet.