Use the image to answer the question. 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. (1 point) ft.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
The height of the pyramid forms a right triangle with the slant height and half of the length of the base.
Let's call the length of the edge of the square base "x".
Using the Pythagorean theorem, we have:
x^2 + (x/2)^2 = slant height^2
x^2 + (x^2/4) = (436.5ft)^2
Multiplying both sides by 4:
4x^2 + x^2 = (436.5ft)^2 * 4
5x^2 = (436.5ft)^2 * 4
Dividing both sides by 5:
x^2 = (436.5ft)^2 * 4 / 5
Taking the square root of both sides:
x = sqrt((436.5ft)^2 * 4 / 5)
x = 387.3ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base is approximately 387.3 feet.
wrong
Apologies for the mistake. Let's correct our approach.
In a pyramid, the slant height forms a right triangle with the height and a side of the square base. Since the pyramid's slant height, height, and base form a right triangle, we can use the Pythagorean theorem to find the length of the base.
Let's call the length of the base "x".
Using the Pythagorean theorem, we have:
x^2 = slant height^2 - height^2
x^2 = (436.5ft)^2 - (321ft)^2
x^2 = 190,522.25ft^2 - 103,041ft^2
x^2 = 87,481.25ft^2
Taking the square root of both sides:
x = sqrt(87,481.25ft^2)
x ≈ 295.8ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base is approximately 295.8 feet.
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.
In this case, the slant height is 436.5 ft, and the height is 321 ft. We can let the length of the edge of the square base be represented by "x".
Using the Pythagorean theorem, we have:
x^2 = (321 ft)^2 + (h)^2
x^2 = (321 ft)^2 + (436.5 ft)^2
Now we can solve for x by taking the square root of both sides:
x = √[(321 ft)^2 + (436.5 ft)^2]
Using a calculator, we find that:
x ≈ 545.7 ft
Therefore, the length of the edge of the square base of The Pyramid is approximately 545.7 ft, rounded to the nearest tenth.