A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the

Question

2 years ago

14

A new building in the shape of a square pyramid is to be constructed. The slant height will be five times the side length of the

base. There will be between 20,000 square feet and 50,000 square feet of construction material used for the outside of the building. What would be the maximum possible side length of the base of the building? Round your answer to the nearest foot.
Please explain how to solve this problem, not just the answer.

Mathematics

2 answers:

mixas84 [53] · Answer 1 · 2022-12-01T22:02:29+03:00

mixas84 [53]2 years ago

7 0

Answer:

48

Step-by-step explanation:

If we use above fourty eight.

49 * 245 = 12005.(slant area) 12005 * 4 = 48020.

(base area) 49 * 49 = 2401. 2401+48020 = 50421. (Over our limit?!?)

Temka [501] · Answer 2 · 2022-12-01T19:34:39+03:00

The area of the square pyramid building is the amount of space on it

The maximum base length of the building is 67.42 cm

<h3>How to determine the maximum side length?</h3>

The given parameters are:

Base = b

Slant height (l) = 5b

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * b * 5b

Evaluate the product

L = 10b^2

The total surface area is calculated using:

T = L + b^2

So, we have:

T = 10b^2 + b^2

Evaluate the sum

T = 11b^2

The maximum surface area is 50,000 square feet

So, we have:

11b^2 = 50000

Divide both sides by 11

b^2 = 50000/11

Take the square root of both sides

b = 67.42

Hence, the maximum base length of the building is 67.42 cm