Question

Use the image to answer the question.

A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.

The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth.

(1 point)

step-by-step bot

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the edge of the square base, let's use the Pythagorean theorem.

The Pythagorean theorem states that the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the lengths of the other two sides (in this case, the height and the length of one edge of the square base).

So, we have:

slant height^2 = height^2 + edge length^2

Replacing the values given in the problem:

436.5^2 = 321^2 + edge length^2

Simplifying:

191,202.25 = 103,041 + edge length^2

Subtracting 103,041 from both sides:

88,161.25 = edge length^2

Taking the square root of both sides:

edge length ≈ √(88,161.25) ≈ 297.0 feet

Therefore, the length of the edge of the square base is approximately 297.0 feet, rounded to the nearest tenth.