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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 of the pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
In this case, the height (321 ft) is the leg of the right triangle, the slant height (436.5 ft) is the hypotenuse, and the length of the edge of the square base is the other leg, which we will call "l".
Using the Pythagorean theorem, we can set up the following equation:
l^2 + 321^2 = 436.5^2
Now we can solve for "l".
l^2 + 321^2 = 436.5^2
l^2 = 436.5^2 - 321^2
l^2 = 190368.25 - 103041
l^2 = 87327.25
Taking the square root of both sides to solve for "l", we get:
l = √87327.25
Using a calculator, we find that l is approximately 295.7ft (rounded to the nearest tenth).
Therefore, the length of the edge of the square base of the pyramid is approximately 295.7 ft.
To find the length of the edge of the square base, we can use the Pythagorean Theorem. The slant height, height, and the length of the edge of the base form a right triangle.
Let's use "x" to represent the length of the edge of the square base.
Using the Pythagorean Theorem, we have:
x^2 + (321 ft)^2 = (436.5 ft)^2
Simplifying this equation, we have:
x^2 + 103,041 ft^2 = 190,822.25 ft^2
Subtracting 103,041 ft^2 from both sides, we have:
x^2 = 87,781.25 ft^2
Taking the square root of both sides, we have:
x ≈ 296.2 ft
Therefore, the length of the edge of the square base is approximately 296.2 feet.
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 length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with the height as one of the sides and the slant height as the hypotenuse. The length of the edge of the square base is the other side of the triangle.
Let's call the length of the edge of the square base "l". According to the Pythagorean theorem, we have:
l^2 + 321^2 = 436.5^2
Now we can solve for "l" by rearranging the equation:
l^2 = 436.5^2 - 321^2
l^2 = 190225.25 - 103041
l^2 = 87284.25
To find "l", we can take the square root of both sides of the equation:
l = √87284.25
l ≈ 295.5
Therefore, the length of the edge of the square base is approximately 295.5 feet.