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)
___ in ft.
The length of the edge of the square base can be found using the Pythagorean Theorem. Let's call the length of the edge of the square base "x".
According to the Pythagorean Theorem, the square of the slant height (436.5 ft) is equal to the sum of the squares of the height (321 ft) and half the length of the side (x/2):
(436.5)^2 = (321)^2 + (x/2)^2
189922.25 = 103041 + (x/2)^2
x^2/4 = 188881.25
x^2 = 755525
x = √755525 ≈ 868.9 ft
Therefore, the length of the edge of the square base is approximately 868.9 feet.
That's incorrect...
Apologies for the incorrect answer. Let me recalculate.
We can use the concept of similar triangles to find the length of the edge of the square base. The ratio of the slant height to the height of the pyramid should be the same as the ratio of the slant height to the length of the edge of the square base.
Therefore, we can set up the following proportion:
slant height / height = slant height / length of edge
436.5 ft / 321 ft = 436.5 ft / x
Now we can cross-multiply and solve for x:
321 ft * 436.5 ft = 436.5 ft * x
140020.5 ft^2 = 436.5 ft * x
Dividing both sides by 436.5 ft:
140020.5 ft^2 / 436.5 ft = x
x ≈ 320.6 ft
Therefore, the length of the edge of the square base is approximately 320.6 feet.