he 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
No
To find the length of the edge of the square base of the pyramid, we can use the Pythagorean Theorem.
Let's denote the length of the edge of the square base as "x."
According to the Pythagorean Theorem, the equation is:
x^2 + (x/2)^2 = (slant height)^2
x^2 + (x^2/4) = 436.5^2
Multiplying through by 4 to remove the denominator:
4x^2 + x^2 = 436.5^2 * 4
Combining like terms:
5x^2 = 436.5^2 * 4
Dividing both sides by 5:
x^2 = (436.5^2 * 4) / 5
Taking the square root of both sides:
x ≈ √[(436.5^2 * 4) / 5]
x ≈ √[(191,102.25 * 4) / 5]
x ≈ √(764,409 / 5)
x ≈ √152,881.8
x ≈ 391.1
Rounding to the nearest tenth, the length of the edge of the square base is approximately 391.1 feet.