Adam is standing at the top ofbuilding A with the height of 20m tall. Ben is standing at the top of building B with the height of 35m tall. Distance between building A & building B is 36m.

What is the shortest distance between Adam and Ben?

42m

39m

36m

45m

To find the shortest distance between Adam and Ben, we can model this situation using the Pythagorean theorem. Imagine that the two buildings and the line connecting Adam and Ben form a right triangle.

- Building A has a height of 20 meters (height from Adam to the ground).
- Building B has a height of 35 meters (height from Ben to the ground).
- The distance between the buildings (the horizontal distance between their bases) is 36 meters.

The difference in height between the two buildings is:

\[
\text{Difference in height} = 35 \, \text{m} - 20 \, \text{m} = 15 \, \text{m}
\]

Now, the shortest distance between Adam and Ben is the hypotenuse of the right triangle formed by:

- The difference in height (15 meters),
- The horizontal distance between the buildings (36 meters).

Using the Pythagorean theorem:

\[
\text{Shortest distance}^2 = (\text{Horizontal distance})^2 + (\text{Difference in height})^2
\]

Substituting the values:

\[
\text{Shortest distance}^2 = 36^2 + 15^2
\]

\[
\text{Shortest distance}^2 = 1296 + 225 = 1521
\]

Taking the square root:

\[
\text{Shortest distance} = \sqrt{1521} = 39 \, \text{m}
\]

So, the shortest distance between Adam and Ben is **39 meters**.

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Do you want more details, or have any questions?

Here are 5 related questions to consider:
1. How would the shortest distance change if the height of building A were increased?
2. What if the horizontal distance between the buildings was increased by 10 meters?
3. Can the Pythagorean theorem be used to calculate distances in 3D space?
4. What if both buildings were the same height—what would the shortest distance be then?
5. How can trigonometric functions help in finding the shortest distance in similar problems?

**Tip:** Always ensure you're working with the correct side lengths when applying the Pythagorean theorem to avoid calculation errors.

Learn how to calculate the shortest distance between Adam and Ben using the Pythagorean theorem. Understand the relationship between the heights of buildings A and B and the horizontal distance between them. Suitable for students in Grades 7-9.

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