Question

A rectangular park that measures 30 yards by 40 yards will have a diagonal path built. How long will the path be? Round your answer to the nearest tenth.

Answer 1

To find the length of the diagonal path in the rectangular park, we can use the Pythagorean theorem. The formula for the diagonal \( d \) in a rectangle with width \( w \) and length \( l \) is:

\[
d = \sqrt{w^2 + l^2}
\]

In this case, the width \( w = 30 \) yards and the length \( l = 40 \) yards.

Now, substituting these values into the formula:

\[
d = \sqrt{30^2 + 40^2}
\]
\[
d = \sqrt{900 + 1600}
\]
\[
d = \sqrt{2500}
\]
\[
d = 50
\]

Thus, the length of the diagonal path is \( 50 \) yards.

Rounding to the nearest tenth, the answer remains:

\[
\text{Length of the path} = 50.0 \text{ yards}
\]