Vicente has a fishing rod of 3.25 meters long. He wants to fit it into an elevator that is 1.5 meters wide, 1.8 meters deep and 2.3 meters high. Can he fit the rod into the elevator without bending it? We need to find the length of the longest straight line that can fit inside the elevator.

1. Problem Description

Vicente has a fishing rod of 3.25 meters long. He wants to fit it into an elevator that is 1.5 meters wide, 1.8 meters deep and 2.3 meters high. Can he fit the rod into the elevator without bending it? We need to find the length of the longest straight line that can fit inside the elevator.

2. Solution Steps

The longest straight line that can fit inside a rectangular prism is the space diagonal. We can find the length of the space diagonal using the formula:

$d = \sqrt{l^2 + w^2 + h^2}$

where $l$ is the length, $w$ is the width, and $h$ is the height of the rectangular prism.

In this case, $l = 1.8$ meters, $w = 1.5$ meters, and $h = 2.3$ meters.

Plugging these values into the formula, we get:

$d = \sqrt{(1.8)^2 + (1.5)^2 + (2.3)^2}$

$d = \sqrt{3.24 + 2.25 + 5.29}$

$d = \sqrt{10.78}$

$d \approx 3.28$ meters.

Since the length of the fishing rod is 3.25 meters and the length of the space diagonal is approximately 3.28 meters, the rod will fit into the elevator.

3. Final Answer

Yes, the rod will fit.

$d = \sqrt{1.8^2 + 1.5^2 + 2.3^2} \approx 3.28$