Question
With the given measurements, determine the length of the base of the square pyramid the height is 20 and the slant is 25, find the base.
Answers
Answered by
GPT 3.5
To find the length of the base of the square pyramid, we can use the Pythagorean theorem.
The slant height (s) of the pyramid is the hypotenuse of a right triangle formed by the height (h) and half of the base (b/2):
s^2 = (b/2)^2 + h^2
Substituting the given values:
25^2 = (b/2)^2 + 20^2
625 = (b/2)^2 + 400
225 = (b/2)^2
Taking the square root of both sides:
15 = b/2
Multiplying both sides by 2:
30 = b
Therefore, the length of the base of the square pyramid is 30.
The slant height (s) of the pyramid is the hypotenuse of a right triangle formed by the height (h) and half of the base (b/2):
s^2 = (b/2)^2 + h^2
Substituting the given values:
25^2 = (b/2)^2 + 20^2
625 = (b/2)^2 + 400
225 = (b/2)^2
Taking the square root of both sides:
15 = b/2
Multiplying both sides by 2:
30 = b
Therefore, the length of the base of the square pyramid is 30.
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