A room has dimensions 3m(height) X 3.7m X 4.3m. A fly starting at one corner flies arougn, ending up at the diagonally opposite corner.

If the fly walks rather than flies what is the lenght of the shortest path it can take?

the book says that the answer is 7.96m



Redraw the box, moving the walls to the same flat surface (like you were making the box from construction paper). Now draw a line from the right most corner through to bottom corner on the third panel.

distance^2= (3^3 + ( 3.7+4.3)^2) I don't get the text answer.

Well, it seems like the fly is in a bit of a pickle, huh? To find the length of the shortest path it can take, let's use some clowny math!

First, let's imagine unfolding the room, like trying to flatten a crumpled piece of paper. Now, we have a rectangle instead of a box. The fly needs to go from one corner to the diagonally opposite corner.

We can then draw a straight line from the rightmost corner to the bottom corner on the third panel. This line represents the shortest path the fly can take.

Using some math magic, we can calculate the length of this line. Using the Pythagorean theorem, the distance can be found by taking the square root of the sum of the squares of the dimensions.

In this case, the calculation would look like this:
Length = √(3^2 + (3.7 + 4.3)^2)

Simplifying further:
Length = √(9 + 8^2)
Length = √(9 + 64)
Length = √73
Length ≈ 8.54m

Oh no! It seems that my clowny math didn't match the answer in the book. So, either the book made a mistake, or I did in my calculations. But remember, in Clown world, there's always room for a little bit of laughter and confusion!

To find the length of the shortest path the fly can take if it walks along the walls, we need to consider the diagonal distance of the room. Let's calculate it step by step.

1. First, draw a diagram of the room with the dimensions provided: 3m (height), 3.7m (length), and 4.3m (width).

2. Then, imagine folding the walls onto a flat surface, so that the walls are on the same plane.

3. Next, draw a line from the top-right corner to the bottom-left corner on the folded surface.

4. This line represents the shortest path the fly can walk, as it goes diagonally across the room.

5. To calculate the distance of this line, we can use the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

6. In this case, the height of the triangle is 3m, and the length and width, when added together, form the base of the triangle. So the length of the base is 3.7m + 4.3m = 8m.

7. Applying the Pythagorean theorem, we have: distance^2 = 3^2 + 8^2 = 9 + 64 = 73.

8. Finally, we take the square root of 73 to find the actual distance: distance = √73.

9. Evaluating this expression, you'll find that the length of the shortest path the fly can take is approximately 8.544 meters, not 7.96 meters as stated in the book.

So, based on the calculations, it seems that either the book made an error or there might be more information or context that needs to be considered for the given answer.

To find the length of the shortest path the fly can take, we need to consider that the fly can only move on the surface of the walls. The fly cannot move through the solid parts of the room.

To visualize this, you can imagine unfolding the room into a flat surface like construction paper. By doing so, the dimensions of the room will change.

Let's go through the process step by step:
1. Start by moving the walls of the room to a single flat surface. Notice that two dimensions (3.7m and 4.3m) will become the base of this surface, while the other dimension (3m) represents the height.

|_ 3.7m _|_ 4.3m _|

2. Next, draw a line from the top right corner of the surface to the bottom left corner. This line represents the shortest path the fly can take.

|_ 3.7m _|_ 4.3m _|
| |
| |
|____________|
|---- 7.96m ---------|

3. Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the length of the line we drew. In this case, one side is 3m and the other side is the sum of 3.7m and 4.3m (because they form the base of the surface).

distance^2 = (3^2 + (3.7 + 4.3)^2)
= (9 + 8^2)
= (9 + 64)
= 73

4. Finally, to find the length of the shortest path, we take the square root of the calculated distance^2.

shortest path = square root of 73
≈ 8.54m

So, according to the calculations, the shortest path the fly can take is approximately 8.54m, not 7.96m as stated in the book.