The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5
Find the length of the edge of the square base. Round the answer to the nearest tenth.
There can’t be a decimal in the answer, round to the nearest tenth, and make sure it’s right!
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 (in this case, the slant height) is equal to the sum of the squares of the other two sides.
Let's denote the length of each side of the square base as "x".
Using the Pythagorean theorem, we can set up the following equation:
x^2 + x^2 = 436.5^2
Simplifying this equation:
2x^2 = 436.5^2
Dividing both sides by 2:
x^2 = (436.5^2)/2
Taking the square root of both sides (and rounding to the nearest tenth):
x ≈ √((436.5^2)/2) ≈ 308.5
Therefore, the length of the edge of the square base is approximately 308.5.
It’s incorrect, there can’t be a decimal in the answer!!!
I apologize for the previous incorrect response. Let's solve the problem again:
To find the length of the edge of the square base, we know that the slant height is the hypotenuse of a right triangle.
Let's denote the length of each side of the square base as "x".
Using the Pythagorean theorem, we can set up the following equation:
x^2 + x^2 = 436.5^2
Simplifying this equation:
2x^2 = 436.5^2
Dividing both sides by 2:
x^2 = (436.5^2)/2
Taking the square root of both sides (and rounding to the nearest whole number):
x ≈ √((436.5^2)/2) ≈ 308
Therefore, the length of the edge of the square base is approximately 308.
That’s still wrong!
Apologies for the mistake. Let's try solving it again:
To find the length of the edge of the square base, we can use the properties of a right triangle. The height (h) of the pyramid forms a right triangle with half the length of the diagonal of the square base.
Let's denote the length of each side of the square base as "x". We can consider half the diagonal of the square base as the hypotenuse of this right triangle.
Using the Pythagorean theorem, we have:
(0.5 * diagonal)^2 = height^2 + (0.5 * side length)^2
Substituting the given values, we have:
(0.5 * diagonal)^2 = 321^2 + (0.5 * x)^2
0.5^2 * diagonal^2 - 0.5^2 * x^2 = 321^2
Simplifying further:
0.25 * diagonal^2 - 0.25 * x^2 = 321^2
Now, we can substitute the given values for the diagonal and the height:
0.25 * 436.5^2 - 0.25 * x^2 = 321^2
Simplifying this equation gives us:
95443.5625 - 0.25 * x^2 = 103041
Subtracting 95443.5625 from both sides:
-0.25 * x^2 = 103041 - 95443.5625 = 7597.4375
Dividing both sides by -0.25:
x^2 = -7597.4375 / -0.25 = 30389.75
Taking the square root of both sides (rounding to the nearest whole number):
x ≈ √30389.75 ≈ 174.3
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 174.3.
Incorrect, again. Make sure it’s the right answer!
Apologies for the repeated mistakes. Let's solve the problem correctly this time.
To find the length of the edge of the square base, we can use the properties of a right triangle formed by the height, slant height, and half the diagonal of the square base.
Let's denote the length of each side of the square base as "x".
Using the Pythagorean theorem, we have:
x^2 + (0.5 * diagonal)^2 = slant height^2
Substituting the given values, we have:
x^2 + (0.5 * diagonal)^2 = 436.5^2
Now, let's substitute the given values for the height (321 ft.) and slant height (436.5 ft.):
x^2 + (0.5 * diagonal)^2 = 436.5^2
x^2 + (0.5 * x)^2 = 436.5^2
Expanding and simplifying this equation:
x^2 + 0.25 * x^2 = 436.5^2
1.25 * x^2 = 436.5^2
Dividing both sides by 1.25:
x^2 = (436.5^2)/1.25
Taking the square root of both sides (rounding to the nearest tenth):
x ≈ √((436.5^2)/1.25) ≈ 383.1
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 383.1.
Wrong, find the length of the edge of the square base.
I apologize for the repeated incorrect responses. Let's solve the problem correctly this time:
To find the length of the edge of the square base, we can use the properties of a right triangle formed by the height, slant height, and half the length of the diagonal of the square base.
Let's denote the length of each side of the square base as "x".
Using the Pythagorean theorem, we have:
x^2 + (0.5 * diagonal)^2 = slant height^2
Substituting the given values, we have:
x^2 + (0.5 * diagonal)^2 = 436.5^2
Now, let's substitute the given values for the height (321 ft.) and slant height (436.5 ft.):
x^2 + (0.5 * x)^2 = 436.5^2
Expanding and simplifying this equation:
x^2 + 0.25 * x^2 = 436.5^2
1.25 * x^2 = 436.5^2
Dividing both sides by 1.25:
x^2 = (436.5^2)/1.25
Taking the square root of both sides:
x = √((436.5^2)/1.25)
x ≈ 389.3
Therefore, the length of the edge of the square base, rounded to the nearest tenth, is approximately 389.3.