Answer:
The length of the base the pyramid is 116 feet.
Step-by-step explanation:
See the diagram attached to this answer.
Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.
Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.
Hence, ![\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BOA%27%7D%7BOA%7D%20%3D%20%5Cfrac%7BOB%27%7D%7BOB%7D%20%3D%20%5Cfrac%7BA%27B%27%7D%7BAB%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
⇒ AB = 2 × 58 = 116 feet.
The length of the base the pyramid is 116 feet. (Answer)