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)
By using the Pythagorean theorem, we can find the length of the edge of the square base.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the slant height is 436.5 ft, and the height is 321 ft. Let the length of the edge of the square base be l.
We can set up the equation:
l^2 + 321^2 = 436.5^2
Simplifying:
l^2 + 103,041 = 190,622.25
Moving the constant term to the other side:
l^2 = 190,622.25 - 103,041
l^2 = 87,581.25
Taking the square root of both sides:
l = √87,581.25
l ≈ 295.9 ft
Therefore, the length of the edge of the square base is approximately 295.9 feet.