To find the length of the edge of the square base using the Pythagorean theorem, we can consider the right triangle formed by the height, slant height, and half of the base of the pyramid.
Let's call the length of the edge of the square base "x."
Using the Pythagorean theorem, we have:
x² = (1/2x)² + 321².
Simplifying the equation, we get:
x² = (1/4)x² + 321².
To get rid of the fraction, we can multiply the entire equation by 4, giving:
4x² = x² + (321²) × 4.
Expanding the equation further, we have:
4x² = x² + 411,041.
Combining like terms:
4x² - x² = 411,041.
Simplifying:
3x² = 411,041.
Dividing both sides by 3:
x² = 411,041 / 3.
Taking the square root of both sides:
x ≈ √(411,041 / 3).
Calculating the square root:
x ≈ √137,013.6667.
Rounding to the nearest tenth:
x ≈ 370.1 ft.
Therefore, the length of the edge of the square base of the pyramid is approximately 370.1 feet.
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
use the Pythagorean theorem
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