Question

If a pyramid’s height is 321, and the slant height is 436.5, what’s the length of the edge of the square base? Round to nearest tenth

Answer 1

No

Answer 2

Let's use the Pythagorean theorem to find the length of the edge of the square base.

The Pythagorean theorem 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 height of the pyramid is one of the sides of the right triangle, the slant height is the hypotenuse, and the length of the edge of the square base is the other side.

Using the Pythagorean theorem:
(length of edge of square base)^2 + (height)^2 = (slant height)^2

Let's substitute the given values into the equation and solve for the length of the edge of the square base:

(length of edge of square base)^2 + (321)^2 = (436.5)^2

(length of edge of square base)^2 = (436.5)^2 - (321)^2

(length of edge of square base)^2 = 190225 - 103041

(length of edge of square base)^2 = 87216

Taking the square root of both sides to solve for the length of the edge of the square base:

length of edge of square base = sqrt(87216)

length of edge of square base ≈ 295.1

Rounding to the nearest tenth, the length of the edge of the square base is approximately 295.1.

Answer 3

Apologies for the error. Let's correct the calculation.

Using the Pythagorean theorem:
(length of edge of square base)^2 + (height)^2 = (slant height)^2

Substituting the given values:
(length of edge of square base)^2 + (321)^2 = (436.5)^2

(length of edge of square base)^2 = (436.5)^2 - (321)^2

(length of edge of square base)^2 = 190522.25 - 103041

(length of edge of square base)^2 = 87481.25

Taking the square root of both sides:
length of edge of square base = sqrt(87481.25)

Rounding to the nearest tenth:
length of edge of square base ≈ 295.6

Therefore, the length of the edge of the square base is approximately 295.6.