Use the image to answer the question.
A square pyramid is shown. Its height is shown with a dotted line labeled 321 feet. Its slant height is shown with a dotted line labeled 436.5 feet. The variable l is shown along one of the edges of the square base.
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)
To find the length of the edge of the square base, we can use the Pythagorean theorem since we have the height and slant height of the pyramid.
Let's label the length of the edge of the square base as 'l'.
We can form a right triangle with one leg as half the length of the edge of the square base, and the hypotenuse as the slant height of the pyramid.
Using the Pythagorean theorem, we have:
(l/2)^2 + 321^2 = 436.5^2
Simplifying:
(l/2)^2 = 436.5^2 - 321^2
(l/2)^2 = 190174.25 - 103041
(l/2)^2 = 87133.25
l/2 = sqrt(87133.25)
l/2 ≈ 295.2
l ≈ 2 * 295.2
l ≈ 590.4
Therefore, the length of the edge of the square base is approximately 590.4 feet (rounded to the nearest tenth).
wrong
I apologize for the mistake. Let's try again.
Given that the height of the pyramid is 321 ft and the slant height is 436.5 ft, we can use the Pythagorean theorem to find the length of the edge of the square base.
Let's label the length of the edge of the square base as 'l'.
We can form a right triangle with one leg as half the length of the edge of the square base (l/2), the height of the pyramid (321 ft), and the slant height of the pyramid (436.5 ft).
Using the Pythagorean theorem, we have:
(l/2)^2 + 321^2 = 436.5^2
Simplifying:
(l^2)/4 + 321^2 = 436.5^2
(l^2)/4 + 103041 = 190174.25
(l^2)/4 = 87133.25
l^2 = 87133.25 * 4
l^2 = 348533
Taking the square root of both sides:
l ≈ √348533
l ≈ 590.4 ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base is approximately 590.4 feet (rounded to the nearest tenth).
To find the length of the edge of the square base, we can use the Pythagorean theorem. In a right triangle with the base edge of the square pyramid (l), the height (321 ft), and the slant height (436.5 ft), the Pythagorean theorem states that the square of the hypotenuse (436.5 ft) is equal to the sum of the squares of the other two sides:
l^2 + 321^2 = 436.5^2
We can now solve this equation to find the value of l.
l^2 + 103041 = 190522.25
l^2 = 190522.25 - 103041
l^2 = 87481.25
To find the length of the edge, we take the square root of both sides:
√(l^2) = √(87481.25)
l = √87481.25
Now, calculate the square root of 87481.25 to find the value of l:
l ≈ 295.4
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 295.4 feet.