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. what is the length of the ledge of the square base?
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let's represent the length of the edge of the square base as "x".
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:
x^2 + x^2 = (436.5)^2
Simplifying this equation, we get:
2x^2 = 190660.25
Dividing both sides of the equation by 2, we have:
x^2 = 95330.125
To solve for x, we take the square root of both sides of the equation:
x = √95330.125
x ≈ 308.8 ft.
Therefore, the length of the edge of the square base of the Pyramid is approximately 308.8 feet.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the pyramid is one of the sides, and the slant height is the hypotenuse. We can use these values to find the length of the edge of the square base.
Let's call the length of the edge of the square base "x".
By applying the Pythagorean theorem, we can set up the following equation:
x^2 + (321/2)^2 = 436.5^2
Simplifying this equation, we have:
x^2 + 51529.25 = 190652.25
Next, we subtract 51529.25 from both sides:
x^2 = 139123
Finally, we take the square root of both sides to solve for x:
x = √139123
Using a calculator, we find that √139123 ≈ 372.8
Therefore, the length of the edge of the square base is approximately 372.8 feet.
To find the length of the edge of the square base of the Pyramid in Memphis, Tennessee, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (which in this case is the slant height) is equal to the sum of the squares of the other two sides.
Let's call the length of the edge of the square base "x". We can set up the following equation using the Pythagorean theorem:
x^2 + x^2 = 436.5^2
Simplifying the equation, we get:
2x^2 = 436.5^2
To find the value of x^2, we divide both sides of the equation by 2:
x^2 = 436.5^2 / 2
Using a calculator, we can calculate that x^2 is approximately equal to 95429.0625.
Now, we can take the square root of both sides of the equation to find the value of x:
x = sqrt(95429.0625)
Using a calculator, we find that x is approximately equal to 308.9.
Therefore, the length of the edge of the square base of the Pyramid in Memphis, Tennessee is approximately 308.9 feet when rounded to the nearest tenth.