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.
thats wrong
935.9
nvm -_-
To find the length of the edge of the square base, we can use the Pythagorean theorem.
In a right triangle with the height (h), slant height (l), and base edge (b), the Pythagorean theorem can be used as:
l² = b² + h²
We know the height (h) is 321 ft and the slant height (l) is 436.5 ft.
Plugging these values into the equation, we get:
436.5² = b² + 321²
Solving for b, we have:
b² = 436.5² - 321²
b² = 190445.22 - 103041
b² = 87404.22
Taking the square root of both sides, we find:
b ≈ √(87404.22)
b ≈ 295.7 ft
Therefore, the length of the edge of the square base is approximately 295.7 ft (rounded to the nearest tenth).
Let's use the Pythagorean theorem to find the length of one side of the square base.
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 slant height is the hypotenuse, the height is one of the sides, and the length of the edge of the square base is the other side.
Let's call the length of the edge of the square base "x".
Using the Pythagorean theorem, we can write the equation:
x^2 + height^2 = slant height^2
Plugging in the given values, we get:
x^2 + 321^2 = 436.5^2
Simplifying the equation, we have:
x^2 + 103041 = 190392.25
Subtracting 103041 from both sides of the equation, we get:
x^2 = 87351.25
Taking the square root of both sides, we have:
x ≈ 295.6
Therefore, the length of the edge of the square base is approximately 295.6 feet.
To find the length of the edge of the square base of the Pyramid in Memphis, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the Pyramid is the hypotenuse, the height is one of the sides, and the length of the edge of the square base is the other side.
Let's denote the height of the Pyramid as h, the slant height as l, and the length of the edge of the square base as s.
According to the Pythagorean Theorem, we have:
s^2 + h^2 = l^2
Substituting the given values into this equation:
s^2 + 321^2 = 436.5^2
Now, we can solve the equation to find the value of s.
s^2 + 103041 = 190522.25
Rearranging the equation:
s^2 = 190522.25 - 103041
s^2 = 87481.25
To find the length of the edge of the square base, we need to take the square root of both sides:
s = √87481.25
Using a calculator, we find the square root of 87481.25 to be approximately 295.9 (rounded to one decimal place).
Therefore, the length of the edge of the square base of the Pyramid in Memphis is approximately 295.9 ft.