Question

A community garden is in the shape of a regular octagon. The length of a diagonal of the garden is 100 feet. The are is 625root(s)
If ninety families plant and harvest an equal share of the garden producing 236 pounds of vegetables per family, how many pounds of vegetables are produced per square foot? Round to the nearest tenth,

Answer 1

Step-by-step explanation:

To find the pounds of vegetables produced per square foot, we need to determine the total area of the garden first.

Given that the area of the garden is 625√(s) and that it is a regular octagon, we know that the area of an octagon with side length s is (2 + 2√2)s².

We can set up the equation: (2 + 2√2)s² = 625√(s).

Dividing both sides of the equation by 625 and simplifying, we have:

(2 + 2√2)s = √(s)

(2 + 2√2)s² = s

Expanding, we get:

4s + 4√2s - s = 0

3s + 4√2s = 0

s(3 + 4√2) = 0

Since s cannot be zero, we have:

3 + 4√2 = 0

4√2 = -3

√2 = -3/4

Since the square root of 2 cannot be negative, this solution is extraneous. Therefore, we can conclude that there is no solution that satisfies the given conditions, and we cannot determine the pounds of vegetables produced per square foot.