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)
ft.
dont answer bot GPT3.5
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 hypotenuse (c, in this case the slant height) is equal to the sum of the squares of the other two sides (a and b, in this case the height and one-half the length of the base).
In this case, the slant height (c) is given as 436.5 ft and the height (a) is given as 321 ft. We can find the length of one-half the base (b) by rearranging the formula:
b = √(c^2 - a^2)
Substituting the given values:
b = √(436.5^2 - 321^2)
Now we can calculate the length of one-half the base using a calculator or math software. The square root of (436.5^2 - 321^2) is approximately 332.5 ft.
Since the question asks for the length of the full edge of the square base, we multiply one-half the base length by 2:
Length of the edge of the square base = 2 * 332.5 ft = 665 ft (rounded to the nearest tenth)
Therefore, the length of the edge of the square base of the pyramid is approximately 665 ft.
To find the length of the edge of the square base, we can use the Pythagorean theorem.
The slant height (hypotenuse) is 436.5 ft, and the height (one of the legs) is 321 ft. Let's denote the length of the edge of the square base as "l".
Using the Pythagorean theorem, we have the equation:
l^2 = (436.5)^2 - (321)^2
l^2 = 190,522.25 - 103,041
l^2 = 87,481.25
Taking the square root of both sides, we find:
l ≈ 295.8 ft.
Therefore, the length of the edge of the square base is approximately 295.8 ft.
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 hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the slant height of the pyramid as the hypotenuse, with a length of 436.5 feet. The height of the pyramid is one of the other sides, with a length of 321 feet. The length of the edge of the square base is the second side.
We can set up the equation as follows:
length of the edge of the square base^2 + height^2 = slant height^2
Let's substitute the given values:
l^2 + 321^2 = 436.5^2
We can solve this equation for the length of the edge of the square base (l):
l^2 + 321^2 = 436.5^2
l^2 + 103041 = 190502.25
l^2 = 87461.25
l ≈ √87461.25
l ≈ 295.5
Therefore, the length of the edge of the square base of the pyramid is approximately 295.5 feet, rounded to the nearest tenth.