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.
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.
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.
A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth. (1 point)
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 (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In this case, let's call the length of each side of the square base "x". We can set up the equation:
x^2 + x^2 = 436.5^2
Simplifying:
2x^2 = 436.5^2
Dividing both sides by 2:
x^2 = 436.5^2 / 2
Taking the square root of both sides to solve for x:
x = √(436.5^2 / 2) ≈ 308.9
Therefore, the length of the edge of the square base is approximately 308.9 feet, rounded to the nearest tenth.
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) is equal to the sum of the squares of the other two sides (a and b).
In this case, the height of the pyramid (321 ft.) is the vertical side, the slant height (436.5 ft.) is the hypotenuse, and the length of the edge of the square base is one of the other two sides.
Let's label the length of the edge of the square base as "x".
We can set up the equation as follows:
x^2 + 321^2 = 436.5^2
Simplifying the equation:
x^2 + 103041 = 190772.25
Subtracting 103041 from both sides:
x^2 = 876731.25
Taking the square root of both sides to solve for x:
x = √876731.25
x ≈ 936.5
Therefore, the length of the edge of the square base is approximately 936.5 feet, rounded to the nearest tenth.
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 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 of a right triangle, with the height of the pyramid as one side and half the length of the base of the pyramid (l/2) as the other side. Applying the Pythagorean theorem:
(slant height)^2 = (height)^2 + (1/2 * base length)^2
(436.5 ft)^2 = (321 ft)^2 + (1/2 * l)^2
Simplifying the equation further:
191,012.25 ft^2 = 103,041 ft^2 + (1/4 * l^2)
Now, let's solve for (1/4 * l^2):
(1/4 * l^2) = 191,012.25 ft^2 - 103,041 ft^2
(1/4 * l^2) = 87,971.25 ft^2
Now, multiply both sides of the equation by 4 to isolate l^2:
l^2 = 4 * 87,971.25 ft^2
l^2 = 351,885 ft^2
Finally, take the square root of both sides to get the length of the edge of the square base:
l = √(351,885 ft^2)
l ≈ 592.8 ft
Therefore, the length of the edge of the square base of the pyramid is approximately 592.8 feet.