The Pythagorean Theorem in Three Dimensions Practice%0d%0aComplete this assessment to review what you've learned. It will not count toward your grade.%0d%0a4 of 54 of 5 Items%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0a%0d%0aQuestion%0d%0aUse the image to answer the question.%0d%0a%0d%0a%0d%0a%0d%0aThe 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.%0d%0a%0d%0a(1 point)%0d%0a ft.q
To find the length of the edge of the square base, we can use the Pythagorean Theorem in three dimensions. 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 (436.5 ft) as the hypotenuse, the height (321 ft) as one of the sides, and the length of the edge of the square base as the other side.
Let's denote the length of the edge of the square base as x.
Using the Pythagorean Theorem, we have:
x^2 + (321 ft)^2 = (436.5 ft)^2
Simplifying the equation:
x^2 + 103,041 ft^2 = 190,822.25 ft^2
x^2 = 190,822.25 ft^2 - 103,041 ft^2
x^2 = 87,781.25 ft^2
Taking the square root of both sides:
x = √87,781.25 ft^2
x ≈ 296.1 ft
Therefore, the length of the edge of the square base is approximately 296.1 feet.
its wrong
I apologize for the mistake. Let's try solving it again.
Using the Pythagorean Theorem, we have:
x^2 = (slant height)^2 - (height)^2
x^2 = (436.5 ft)^2 - (321 ft)^2
x^2 = 190,522.25 ft^2 - 103,041 ft^2
x^2 = 87,481.25 ft^2
Taking the square root of both sides:
x = √87,481.25 ft^2
x ≈ 295.8 ft
Therefore, the length of the edge of the square base is approximately 295.8 feet.
wrong
I apologize for the mistakes made in my previous responses. Let's try solving it again.
We can use the Pythagorean Theorem in three dimensions to solve this problem. Let's denote the length of the edge of the square base as x.
According to the Pythagorean Theorem, we have:
x^2 = (slant height)^2 - (height)^2
x^2 = (436.5 ft)^2 - (321 ft)^2
x^2 = 190,522.25 ft^2 - 103,041 ft^2
x^2 = 87,481.25 ft^2
Taking the square root of both sides:
x = √87,481.25 ft^2
x ≈ 295.5 ft
Therefore, the length of the edge of the square base is approximately 295.5 feet.
To solve this problem, we can use the Pythagorean theorem in three dimensions. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the pyramid is one of the sides, and the slant height is the hypotenuse. We need to find the length of the edge of the square base, which is the other side.
Let's denote the length of the edge of the square base as "x".
Using the Pythagorean theorem, we can set up the equation:
x^2 + 321^2 = 436.5^2
Simplifying the equation:
x^2 + 103041 = 190402.25
Subtracting 103041 from both sides:
x^2 = 87361.25
Taking the square root of both sides:
x = sqrt(87361.25)
Using a calculator, we find that x is approximately 295.5.
Rounding to the nearest tenth, the length of the edge of the square base is approximately 295.5 feet.