- #1

ghostfirefox

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In summary, we can calculate the length of the fourth lateral edge of a pyramid with a square base of side length $s$ and lateral edges of 6016, 2370, and 4350 by using the distance formula and solving a system of equations. The length of the fourth edge is a unique integral value between 4350 and 6016.

- #1

ghostfirefox

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- #2

skeeter

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ghostfirefox said:

let the four corners of the square base with side length $s$ lie in the x y plane with positions

$(0,0,0)$, $(s,0,0)$, $(s,s,0)$, and $(0,s,0)$

let the apex of the pyramid be at position $(a,b,c)$

... assume that edges 6016 and 2370 extend from the opposite tops of the base

using the distance formula between two points in space yields the following equations

$a^2+b^2+c^2 = 6016^2$

$(a-s)^2+(b-s)^2+c^2 = 2370^2$

$(a-s)^2+b^2+c^2=4350^2$

$a^2+(b-s)^2+c^2 = d^2$, where $d$ is the length of the fourth edge

use the system of equations to solve for $d$ ... I get a unique integral value for $d$ such that $4350 < d < 6016$

- #3

ghostfirefox

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I tried to calculate this, but there are too many variables in this system of equations.

- #4

skeeter

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Subtract the 2nd equation from the 4th.

Work the solution for $d$ from the resulting two equations.

To calculate the length of the fourth side edge of a shape, you will need to know the lengths of the other three sides. You can then use the Pythagorean theorem (a² + b² = c²) to find the length of the fourth side.

No, it is not possible to calculate the length of the fourth side edge without knowing the lengths of the other three sides. The Pythagorean theorem requires all three sides to find the length of the fourth side.

The Pythagorean theorem can only be used to find the length of the fourth side edge if the shape is a right triangle. If the shape is not a right triangle, a different formula or method will need to be used to find the length of the fourth side edge.

No, the Pythagorean theorem can only be used to find the length of the fourth side edge of a right triangle. For other shapes, different formulas or methods will need to be used.

The accuracy of the calculation will depend on the accuracy of the measurements of the other three sides. If the measurements are precise, the calculation of the length of the fourth side edge will also be precise. However, if the measurements are not accurate, the calculation will also be inaccurate.

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