We are tasked with finding the length of the edge $AB$ of a pyramid whose vertices are given by their coordinates:

• $A(1, 3, 5)$
• $B(6, 7, 8)$

The length of an edge in 3D space is calculated using the distance formula: $AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

Substituting the values:

$AB = \sqrt{(6 - 1)^2 + (7 - 3)^2 + (8 - 5)^2}$

$AB = \sqrt{5^2 + 4^2 + 3^2}$

$AB = \sqrt{25 + 16 + 9}$

$AB = \sqrt{50}$

$AB \approx 7.07$

Rounding to the nearest whole number:

$AB \approx 7$

Final Answer:

The length of edge $AB$ is 7.

Do you want a step-by-step breakdown or help with related questions? Here are some ideas:

1. What is the distance formula in 3D space?
2. How do we find the length of other edges of the pyramid?
3. What is the general approach for calculating diagonal distances?
4. How does rounding affect the accuracy of calculations?
5. How is the volume of a pyramid computed if its vertices are given?

Tip: Always check the rounding conventions stated in the problem to ensure your final answer matches the requirement.