Eli sculpted this square pyramid out of clay. Its base is 12 inches long on each side and its slant height is 9 inches. What is the approximate height, h, of Eli's pyramid? (the answer includes square root)
Use pythagorean theorem:
c^2 = a^2 + b^2
Substitute the given values, c = slant height, a = 1/2 of length of one side of the base:
9^2 = 6^2 + b^2
b = ?
3 square root of 5
To find the height, h, of Eli's pyramid, we can 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.
In this case, the slant height is the hypotenuse and the height is one of the other sides. The base of the pyramid forms a right triangle with the height and the slant height.
Let's use the Pythagorean Theorem to find h:
h^2 + (12/2)^2 = 9^2
Simplifying the equation:
h^2 + 6^2 = 81
h^2 + 36 = 81
Subtracting 36 from both sides:
h^2 = 45
Taking the square root of both sides:
h = sqrt(45)
Approximating the square root:
h ≈ sqrt(9) * sqrt(5)
h ≈ 3 * sqrt(5)
Therefore, the approximate height of Eli's pyramid is 3 * sqrt(5) inches.
To find the height of Eli's square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid is the hypotenuse of a right triangle, with the base side as one of the legs.
Using the equation of the Pythagorean theorem:
c^2 = a^2 + b^2
In this case:
c = slant height = 9 inches
a = base side = 12 inches
Now, let's solve for b (the height of the pyramid).
b = √(c^2 - a^2)
Substituting the given values:
b = √(9^2 - 12^2)
Calculating this expression:
b = √(81 - 144)
= √(-63)
Since the value under the square root is negative, it means that the pyramid cannot have a real height with the given dimensions.
Therefore, there is no approximate height (h).