Question

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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.
Remaining Attempts : 3
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Answer 1

Half the base and the height form a right triangle with hypotenuse 436.5, so (l/2)^2 + 321^2 = 436.5^2. Thus

l = 2·sqrt(436.5^2 − 321^2) = 2·sqrt(190532.25 − 103041) = 2·sqrt(87491.25) ≈ 591.6 ft.

Answer: 591.6 ft.