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.
It has to be a whole number.
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 side opposite the right angle) 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 legs of the right triangle and the slant height is the hypotenuse. The square of the height is 321^2 = 103,041 and the square of the slant height is 436.5^2 = 190,578.25.
By applying the Pythagorean theorem, we can find the length of the edge of the square base.
Let x be the length of the edge of the square base.
Using the Pythagorean theorem, we have:
x^2 + 321^2 = 436.5^2
x^2 + 103,041 = 190,578.25
x^2 = 190,578.25 - 103,041
x^2 = 87,537.25
Taking the square root of both sides, we get:
x = √87,537.25
x ≈ 295.9
Rounding the answer to the nearest tenth, the length of the edge of the square base is approximately 295.9 feet.
That’s wrong! The answer can’t have a decimal in it.
I apologize for the mistake in my previous response. Let's redo the calculation without rounding the answer to the nearest tenth.
Using the Pythagorean theorem, we have:
x^2 + 321^2 = 436.5^2
x^2 + 103,041 = 190,578.25
x^2 = 190,578.25 - 103,041
x^2 = 87,537.25
Taking the square root of both sides, we get:
x ≈ √87,537.25
x ≈ 295.82
Rounded to the nearest whole number, the length of the edge of the square base would be approximately 296 feet.
Still incorrect, round to the nearest tenth.
Apologies for the confusion. Let's recalculate and round to the nearest tenth without rounding prematurely.
Using the Pythagorean theorem, we have:
x^2 + 321^2 = 436.5^2
x^2 + 103,041 = 190,578.25
x^2 = 190,578.25 - 103,041
x^2 = 87,537.25
Taking the square root of both sides, we get:
x ≈ √87,537.25
x ≈ 295.88
Rounded to the nearest tenth, the length of the edge of the square base would be approximately 295.9 feet.