To find the length of the edge of the square base, we can use the Pythagorean theorem.
In a square pyramid, the slant height, height, and length of the edge of the base form a right triangle.
Let's denote the length of the edge of the base as "l."
Using the Pythagorean theorem, we can write:
l^2 + (321)^2 = (436.5)^2
l^2 + 103041 = 190622.25
l^2 = 190622.25 - 103041
l^2 = 87581.25
Taking the square root of both sides, we get:
l = √87581.25
l ≈ 296.1
Therefore, the length of the edge of the square base is approximately 296.1 feet.
Question
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.
3 answers
nope step by step bot?
Apologies for the error in the previous response. Here's a revised step-by-step solution:
1. We have the height of the pyramid as 321 feet (labeled in the image) and the slant height as 436.5 feet. Our goal is to find the length of the edge of the square base, denoted as "l."
2. Recognize that the height, slant height, and length of the base edge form a right triangle within the pyramid.
3. Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
4. Apply the Pythagorean theorem to the right triangle formed by the height, the base edge length, and half of one of the diagonals of the base.
l^2 + (321^2 / 2)^2 = 436.5^2
5. Simplify the equation:
l^2 + (102241 / 2)^2 = 190622.25
6. Compute 102241 / 2:
l^2 + 51120.5^2 = 190622.25
7. Square 51120.5:
l^2 + 2612771041 = 190622.25
8. Subtract 2612771041 from both sides:
l^2 = 190622.25 - 2612771041
l^2 = -2612570418.75
9. Since we cannot have a negative length, it appears that there is an error or inconsistency in the given information or calculations. Please double-check the values provided or verify if there are any additional details that could help resolve the discrepancy.
1. We have the height of the pyramid as 321 feet (labeled in the image) and the slant height as 436.5 feet. Our goal is to find the length of the edge of the square base, denoted as "l."
2. Recognize that the height, slant height, and length of the base edge form a right triangle within the pyramid.
3. Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
4. Apply the Pythagorean theorem to the right triangle formed by the height, the base edge length, and half of one of the diagonals of the base.
l^2 + (321^2 / 2)^2 = 436.5^2
5. Simplify the equation:
l^2 + (102241 / 2)^2 = 190622.25
6. Compute 102241 / 2:
l^2 + 51120.5^2 = 190622.25
7. Square 51120.5:
l^2 + 2612771041 = 190622.25
8. Subtract 2612771041 from both sides:
l^2 = 190622.25 - 2612771041
l^2 = -2612570418.75
9. Since we cannot have a negative length, it appears that there is an error or inconsistency in the given information or calculations. Please double-check the values provided or verify if there are any additional details that could help resolve the discrepancy.
6 answers