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

1 answer

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.