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)
ft.
The length of the edge of the square base can be found using the Pythagorean theorem. The slant height, height, and one side of the square base form a right triangle.
Using the Pythagorean theorem, we can set up the equation:
l^2 + 321^2 = 436.5^2
Simplifying that equation:
l^2 + 103041 = 190522.25
Subtracting 103041 from both sides of the equation:
l^2 = 87481.25
Taking the square root of both sides of the equation:
l = √87481.25
Rounding to the nearest tenth:
l ≈ 295.4
The length of the edge of the square base is approximately 295.4 feet.
To find the length of the edge of the square base, we can use the Pythagorean theorem. The formula is:
\[l^2 = (slant\ height)^2 - (height)^2\]
Plugging in the given values:
\[l^2 = 436.5^2 - 321^2\]
Simplifying:
\[l^2 = 190,522.25 - 103,041\]
\[l^2 = 87,481.25\]
To solve for l, we take the square root of both sides:
\[l = \sqrt{87,481.25}\]
Calculating the square root:
\[l \approx 295.7 ft.\]
Therefore, the length of the edge of the square base is approximately 295.7 ft. (rounded to the nearest tenth).
To find the length of the edge of the square base, we can use the Pythagorean theorem. In a square pyramid, the slant height (436.5 ft) is the hypotenuse of a right triangle, with one leg being the height (321 ft) and the other leg being half the length of the edge of the square base we're trying to find.
Let's call the length of the edge of the square base 'l'.
Using the Pythagorean theorem, we can write the equation:
l/2 * l/2 + 321 * 321 = 436.5 * 436.5
Simplifying the equation, we get:
(l * l) / 4 + 103041 = 190622.25
Subtracting 103041 from both sides:
(l * l) / 4 = 87581.25
Multiplying both sides by 4:
l * l = 350325
Taking the square root of both sides:
l = √350325 ≈ 591.6 ft
Therefore, the length of the edge of the square base is approximately 591.6 feet (rounded to the nearest tenth).