1Given l=30 in., w=20 in., h=18 in. , and x=36.1 in., find the length of d. Round the answer to the nearest tenth. (1 point)
2For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r . (1 point) The height of the square pyramid is in.
3The 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) ft.
1 To find the length of d, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (d) is equal to the sum of the squares of the other two sides (l and w).
Using the Pythagorean Theorem, we have:
d^2 = l^2 + w^2
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides, we find:
d = √1300
d ≈ 36.1 in.
2 To find the height of the pyramid (h), we can use the Pythagorean Theorem. We need to find the length of the base's radius (r) first.
Using the Pythagorean Theorem, we have:
(0.5e)^2 = r^2 + s^2
(0.5 * 25)^2 = r^2 + 24^2
12.5^2 = r^2 + 576
156.25 = r^2 + 576
r^2 = 419.75
Taking the square root of both sides, we find:
r ≈ √419.75
Now that we have the value of r, we can find the height (h) using the Pythagorean Theorem again:
h^2 = s^2 - r^2
h^2 = 24^2 - (√419.75)^2
h^2 = 576 - 419.75
h^2 = 156.25
Taking the square root of both sides, we find:
h ≈ √156.25
h ≈ 12.5 in.
Therefore, the height of the square pyramid is 12 in.
3 To find the length of the edge of the square base, we can use the Pythagorean Theorem. We have the height (321 ft.) and the slant height (436.5 ft.).
Using the Pythagorean Theorem, we have:
e^2 = h^2 + s^2
e^2 = 321^2 + 436.5^2
e^2 = 103041 + 190564.25
e^2 = 293605.25
Taking the square root of both sides, we find:
e ≈ √293605.25
e ≈ 541.7 ft.
Therefore, the length of the edge of the square base is approximately 541.7 ft.
there all wrong do it again
I apologize for the incorrect answers in my previous response. Let's go through the questions again:
1. Given l = 30 in., w = 20 in., h = 18 in., and x = 36.1 in., we are asked to find the length of d.
To find the length of d, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (d) is equal to the sum of the squares of the other two sides (l and w).
Using the Pythagorean Theorem, we have:
d^2 = l^2 + w^2
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides, we find:
d ≈ √1300
d ≈ 36.1 in.
Therefore, the length of d is approximately 36.1 in.
2. For the square pyramid, given the lateral edge length (e) is 25 in., and the slant height (s) is 24 in., we are asked to find the height (h) of the pyramid.
First, we need to find the length of the base's radius (r) using the Pythagorean Theorem:
(0.5e)^2 = r^2 + s^2
(0.5 * 25)^2 = r^2 + 24^2
12.5^2 = r^2 + 576
r^2 = 156.25
Taking the square root of both sides, we find:
r ≈ √156.25
r ≈ 12.5 in.
Now that we have the value of r, we can find the height (h) using the Pythagorean Theorem again:
h^2 = s^2 - r^2
h^2 = 24^2 - 12.5^2
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides, we find:
h ≈ √419.75
h ≈ 20.5 in.
Therefore, the height of the square pyramid is approximately 20.5 in.
3. The Pyramid in Memphis, Tennessee has a height of 321 ft., and a slant height of 436.5 ft. We are asked to find the length of the edge of the square base.
Using the Pythagorean Theorem, we have:
e^2 = h^2 + s^2
e^2 = 321^2 + 436.5^2
e^2 = 103041 + 190564.25
e^2 = 293605.25
Taking the square root of both sides, we find:
e ≈ √293605.25
e ≈ 541.7 ft.
Therefore, the length of the edge of the square base is approximately 541.7 ft.
1. To find the length of d, we can use the Pythagorean theorem. 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 have a right triangle with sides of length l, w, and d. Applying the Pythagorean theorem, we have:
d^2 = l^2 + w^2
Substituting the given values, we get:
d^2 = 30^2 + 20^2
d^2 = 900 + 400
d^2 = 1300
Taking the square root of both sides, we have:
d = √1300
Using a calculator, we find that d is approximately 36.06 inches. Rounding to the nearest tenth, we get the length of d as 36.1 inches.
2. To find the height of the square pyramid, we need to find the length of r first. The slant height, s, is the hypotenuse of a right triangle formed by the height, h, and the lateral edge length, e. Using the Pythagorean theorem, we have:
s^2 = r^2 + h^2
We are given that s = 24 inches and e = 25 inches. To find r, we can use the formula:
r = √(s^2 - e^2)
Substituting the values we have:
r = √(24^2 - 25^2)
r = √(576 - 625)
r = √(-49)
We cannot take the square root of a negative number, so it appears there is an error in the problem statement. Please double-check the given values.
3. To find the length of the edge of the square base of the Pyramid in Memphis, we can again use the Pythagorean theorem. The height, slant height, and the edge length of the square base form a right triangle. The side lengths are given as follows: height (h) = 321 ft and slant height (s) = 436.5 ft.
Let the edge length of the square base be x. Applying the Pythagorean theorem, we have:
x^2 = h^2 + s^2
Substituting the given values, we get:
x^2 = 321^2 + 436.5^2
x^2 = 103041 + 190762.25
x^2 = 293803.25
Taking the square root of both sides, we have:
x = √293803.25
Using a calculator, we find that x is approximately 541.6 ft. Rounding to the nearest tenth, we get the length of the edge of the square base as 541.6 ft.