Question

A rectangular garden is 8 feet wide and 15 feet long. A diagonal path cuts through the entire garden. How long is the path?
Responses
A 3 feet3 feet
B 7 feet7 feet
C 13 feet13 feet
D 17 feet17 feet
E 23 feet

Answer 1

To find the length of the diagonal path in the rectangular garden, we can use the Pythagorean theorem.

The formula for the diagonal \(d\) of a rectangle with width \(w\) and length \(l\) is:
\[
d = \sqrt{w^2 + l^2}
\]

In this case, the width \(w\) is 8 feet and the length \(l\) is 15 feet:

\[
d = \sqrt{8^2 + 15^2}
\]

Calculating the squares:
\[
8^2 = 64
\]
\[
15^2 = 225
\]

Now, add the squares:
\[
64 + 225 = 289
\]

Now take the square root:
\[
d = \sqrt{289} = 17
\]

Thus, the length of the diagonal path is **17 feet**.

The correct answer is **D: 17 feet**.