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)
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 square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the slant height (436.5 ft) is the hypotenuse, the height (321 ft) is one of the sides, and the length of the edge of the square base (l) is the other side.
So we can set up the equation as:
l^2 + 321^2 = 436.5^2
Simplifying this equation, we get:
l^2 + 103041 = 190702.25
Subtracting 103041 from both sides gives us:
l^2 = 87661.25
To solve for l, we can take the square root of both sides:
l = √87661.25
Rounding to the nearest tenth, we get:
l ≈ 295.9 ft.
Therefore, the length of the edge of the square base is approximately 295.9 feet.