A rectangular garden is 8 feet wide and 15 feet long. A diagonal path cuts through the entire garden. How long is the path?
To find the length of the diagonal path, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length 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 and width of the garden form the two sides of a right triangle, and the diagonal path is the hypotenuse.
So, let's denote the length of the path as 'd', the width of the garden as 'w' (8 feet), and the length of the garden as 'l' (15 feet).
We can now apply the Pythagorean theorem:
d^2 = w^2 + l^2
Substituting the given values:
d^2 = 8^2 + 15^2
Simplifying:
d^2 = 64 + 225
d^2 = 289
Taking the square root of both sides to find the length of the path:
d = sqrt(289)
d = 17 feet
Therefore, the length of the diagonal path is 17 feet.
Hint:
Isn't this just an application of Pythagoras ??