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???
To find the length of the edge of the square base of the Pyramid, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let's call the length of one side of the square base "x". Now we can set up the equation using the Pythagorean theorem:
x^2 + x^2 = (321 ft)^2
Simplifying this equation, we have:
2x^2 = (321 ft)^2
Now, divide both sides of the equation by 2:
x^2 = (321 ft)^2 / 2
Taking the square root of both sides, we can find the value of x:
x = sqrt((321 ft)^2 / 2)
Using a calculator, we find:
x ≈ 227.6 ft
Therefore, the length of the edge of the square base of the Pyramid is approximately 227.6 ft when rounded to the nearest tenth.