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.
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.
To determine the length of the base of a square pyramid, 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, the slant height of the pyramid acts as the hypotenuse, and the height of the pyramid and one-half of the length of the base act as the other two sides of the right triangle.
Let's label the length of the base as "b", the height as "h", and the slant height as "s".
We know that the height is 20 and the slant height is 25.
Using the Pythagorean theorem, we can write the equation:
s^2 = h^2 + (b/2)^2
Substituting the given values:
25^2 = 20^2 + (b/2)^2
625 = 400 + (b/2)^2
Subtracting 400 from both sides:
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 units.
To find the length of the base of a square pyramid, 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 the case of a square pyramid, the slant height acts as the hypotenuse, and the height and half the length of the base act as the other two sides of the right triangle.
Let's denote the length of the base of the square pyramid as 'b', the height as 'h', and the slant height as 's'.
According to the Pythagorean theorem:
s^2 = h^2 + (b/2)^2
In this problem, we are given that the height (h) is 20 and the slant (s) is 25. We need to find the base (b).
Plugging in the given values into the equation, we get:
25^2 = 20^2 + (b/2)^2
625 = 400 + (b/2)^2
225 = (b/2)^2
Taking the square root of both sides, we have:
15 = b/2
Multiplying both sides by 2, we find:
30 = b
Therefore, the length of the base of the square pyramid is 30 units.