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.
We can use the Pythagorean theorem to find the length of the edge of the square base. The slant height, the height, and the edge of the square base form a right triangle.
Let's denote the length of the edge of the square base as $l$.
Using the Pythagorean theorem, we have:
\[l^2 + 321^2 = 436.5^2\]
Simplifying the equation, we get:
\[l^2 + 103041 = 190522.25\]
Subtracting 103041 from both sides, we get:
\[l^2 = 87481.25\]
Finally, taking the square root of both sides, we find:
\[l \approx \sqrt{87481.25} \approx \boxed{295.8 \text{ feet}}\]
Therefore, the length of the edge of the square base is approximately 295.8 feet.
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 length of the hypotenuse (the slant height in this case) is equal to the sum of the squares of the other two sides.
In this case, the slant height (hypotenuse) is 436.5 ft, and the height (one of the other sides) is 321 ft. Let's label the length of the edge of the square base as "l".
According to the Pythagorean theorem, we can write the equation as:
l^2 + 321^2 = 436.5^2
To find the value of "l", rearrange the equation and solve for "l":
l^2 = 436.5^2 - 321^2
l^2 = 190332.25 - 103041
l^2 = 87351.25
l ≈ √87351.25
l ≈ 295.3 ft
Therefore, the length of the edge of the square base is approximately 295.3 ft.
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 length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the pyramid (436.5 ft) is the hypotenuse, the height (321 ft) is one of the other sides, and we need to find the length of the edge of the square base, which will be the other side.
Let's represent the length of the edge of the square base as l.
According to the Pythagorean theorem, we have:
l^2 + 321^2 = 436.5^2
Now we can solve for l by rearranging the equation:
l^2 = 436.5^2 - 321^2
l^2 = 190322.25 - 103041
l^2 = 87381.25
Taking the square root of both sides, we get:
l ≈ √87381.25
l ≈ 295.4
Therefore, the length of the edge of the square base of the pyramid is approximately 295.4 feet (rounded to the nearest tenth).