The pyramids is an arena in Memphis Tennessee. Its height is 321 ft and its slant height is 435.5. Find the length of the edge of the square base
We can solve this problem by using the Pythagorean theorem.
Let the length of the edge of the square base be x.
The slant height is the hypotenuse of a right triangle formed by the height, the slant height, and half the length of the edge of the square base.
Using the Pythagorean theorem, we have:
x^2 + (321/2)^2 = 435.5^2
Simplifying the equation, we get:
x^2 + 103041/4 = 190110.25
Multiplying both sides by 4 to eliminate the fraction, we get:
4x^2 + 103041 = 760441
Subtracting 103041 from both sides, we get:
4x^2 = 657400
Dividing both sides by 4, we get:
x^2 = 164350
Taking the square root of both sides, we get:
x = √164350
Therefore, the length of the edge of the square base is approximately 405 feet.