Question

Now, we will apply those definitions.

A hungry bunny rabbit hops 20 meters north and then turns and hops 8 meters west in search of tasty flowers to eat.

What is the bunny's distance? Show your work (square root symbol).

Answer 1

To find the bunny's distance from its starting point after hopping, we can use the Pythagorean theorem. The rabbit hops 20 meters north and then 8 meters west, creating a right triangle where:

- One leg of the triangle (north) is 20 meters.
- The other leg of the triangle (west) is 8 meters.

We denote the distance from the starting point to the final position as \(d\). According to the Pythagorean theorem:

\[
d^2 = (20 \, \text{meters})^2 + (8 \, \text{meters})^2
\]

Calculating each term:

\[
(20 \, \text{meters})^2 = 400 \, \text{square meters}
\]

\[
(8 \, \text{meters})^2 = 64 \, \text{square meters}
\]

Adding these two results:

\[
d^2 = 400 + 64 = 464 \, \text{square meters}
\]

Now, taking the square root of both sides to find \(d\):

\[
d = \sqrt{464}
\]

To simplify \( \sqrt{464} \):
- We can factor \(464\):
\[
464 = 16 \times 29
\]
- Thus, we can rewrite it:
\[
d = \sqrt{16 \times 29} = \sqrt{16} \cdot \sqrt{29} = 4\sqrt{29}
\]

Next, we can also determine \( \sqrt{464} \) using a calculator, which is approximately \( 21.54 \) meters.

Therefore, the bunny's distance from its starting point is:

\[
d \approx 4\sqrt{29} \text{ meters} \quad \text{or} \quad d \approx 21.54 \text{ meters}
\]