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)
.
Apologies for the mistake in the calculation. Let's calculate it correctly:
We can use the Pythagorean theorem to solve for the length of the edge of the square base.
The slant height represents the hypotenuse of a right triangle formed by the height, half the length of the base, and the slant height.
Using the Pythagorean theorem, we have:
(height)^2 + (1/2 * length of base)^2 = (slant height)^2
Let's substitute the given values:
(height)^2 + (1/2 * x)^2 = (436.5)^2
Simplifying the equation:
(height)^2 + (1/4 * x^2) = 436.5^2
Subtracting (1/4 * x^2) from both sides:
(height)^2 = 436.5^2 - (1/4 * x^2)
Taking the square root of both sides to isolate the height:
height = √(436.5^2 - (1/4 * x^2))
Now, let's substitute the given values and solve for the height:
height = √(436.5^2 - (1/4 * x^2))
height = √(190512.25 - 0.25x^2)
To find the length of the edge of the square base, we need to solve for x.
Since the height is equal to the height of the pyramid, which is 321 ft, we can substitute this value into the equation:
321 = √(190512.25 - 0.25x^2)
Let's solve for x:
Squaring both sides of the equation:
102841 = 190512.25 - 0.25x^2
Rearranging the equation to isolate the term with x:
0.25x^2 = 190512.25 - 102841
0.25x^2 = 87671.25
Dividing both sides of the equation by 0.25:
x^2 = 350685
Taking the square root of both sides to find x:
x = √350685
Calculating the square root:
x ≈ 591.78
Therefore, the length of the edge of the square base is approximately 591.8 ft. Rounded to the nearest tenth, the answer is 591.8 ft.
We can use the Pythagorean Theorem to solve this problem.
Let x be the length of the edge of the square base.
We can form a right triangle using the slant height, the height, and half the length of the edge of the base, as shown:
[image]
Using the Pythagorean Theorem, we have:
(x/2)^2 + 321^2 = 436.5^2
Simplifying this equation, we get:
(x/2)^2 = 436.5^2 - 321^2
(x/2)^2 ≈ 111,054
Taking the square root of both sides, we have:
x/2 ≈ √111,054 ≈ 333.3
Multiplying both sides by 2, we get:
x ≈ 666.6
Therefore, the length of the edge of the square base is approximately 666.6 ft. Rounded to the nearest tenth, this is 666.6 ft.
666.6 is not the answer
To find the length of the edge of the square base of the Pyramid in Memphis, Tennessee, 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 lengths of the other two sides.
In this scenario, the height of the pyramid (which is perpendicular to the base) and the slant height form a right triangle. We can use the Pythagorean Theorem to solve for the length of the base.
Let's denote the length of the base as "x."
Using the Pythagorean Theorem, we have:
x^2 + 321^2 = 436.5^2
Simplifying the equation, we have:
x^2 + 103041 = 190412.25
Subtracting 103041 from both sides:
x^2 = 87371.25
To solve for x, we need to take the square root of both sides:
√x^2 = √87371.25
x ≈ 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.