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)
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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 (slant height in this case) is equal to the sum of the squares of the lengths of the two other sides. In this case, the slant height is 436.5 feet and the height is 321 feet.
Using the formula, we have:
(Length of edge)^2 + (Height)^2 = (Slant height)^2
Let l represent the length of the edge of the square base:
l^2 + 321^2 = 436.5^2
l^2 + 103041 = 190551.225
l^2 = 190551.225 - 103041
l^2 = 87510.225
l ≈ √87510.225
l ≈ 295.7
Therefore, the length of the edge of the square base is approximately 295.7 feet.