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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.
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 (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. Let's label the length of the edge of the square base as "l".
Using the Pythagorean Theorem, we have:
l^2 + 321^2 = 436.5^2
Simplifying the equation:
l^2 + 103041 = 190542.25
Subtracting 103041 from both sides:
l^2 = 87408.25
Taking the square root of both sides to solve for l:
l ≈ √87408.25
l ≈ 295.4
Therefore, the length of the edge of the square base is approximately 295.4 ft.
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 longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid represents the hypotenuse, and the height represents one of the other sides. The length of the edge of the square base represents the other side.
Let's label the height as 'h' and the length of the edge of the square base as 'l'.
Using the Pythagorean theorem, we have:
slant height^2 = height^2 + length of the edge^2
Substituting the given values, we have:
436.5^2 = 321^2 + l^2
Simplifying the equation, we have:
191079.25 = 103041 + l^2
Subtracting 103041 from both sides, we have:
88038.25 = l^2
To find the length of the edge, we need to take the square root of both sides of the equation:
l = √88038.25
Using a calculator, we find:
l ≈ 296.45
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 296.5 ft.
To find the length of the edge of the square base, we can use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides. In this case, the slant height is 436.5 feet and the height (vertical side) is 321 feet.
Let's label the edge length of the square base as 'x'. Now, we can set up the equation:
x^2 = (321^2) + (436.5^2)
Now we can solve for 'x' by taking the square root of both sides of the equation:
x = √[(321^2) + (436.5^2)]
To find the length of the edge of the square base using a calculator:
1. Square the height value: 321^2 = 103,041
2. Square the slant height value: 436.5^2 = 190,522.25
3. Add the two results together: 103,041 + 190,522.25 = 293,563.25
4. Take the square root of the sum: √293,563.25 ≈ 541.7
Therefore, the length of the edge of the square base is approximately 541.7 feet.