You want to design a set of four congruent pyramids whose combined volume is the same as the volume of a single rectangular pyramid. why values of l and h for the four square pyramids and what values of l, w, and h for the rectangular pyramid will produce identical volumes

As long as rectangular and square pyramids have the same length and height, the condition will be fulfilled if rectangular pyramid's width is four times square pyramid's length.

Step-by-step explanation

Reference

l: length

w: width

h: height

Assumption: rectangular and square pyramids have the same length and height.

Volume of a rectangular pyramid

V1 = (1/3)*l*w*h

Volume of a square pyramid

V2 = (1/3)*l^2*h

We need that V2*4 = V1. So

(1/3)*l^2*h*4 = (1/3)*l*w*h

Simplifying

l*4 = w