maths pyramid question?

Question

Pyramid maths question??
imagine a diagram representing a right pyramid.
the base is a square of side 2x.

The length of each of the slant edges is 8s.rt3.

The height of the pyramid is x cm

calculate the value of x.

(i think the answer is 8... but i want to know how to get there... especially the first few steps)

Answer 1

Let's label the side of the base a, and label the height of the pyramid h.

a = 2x and h = x

Knowing this, you can calculate the height of the triangles which are on the slant sides (do a sketch of a square-based pyramid, you'll see what I mean). Let's label the height of the sides hs.

(hs)^2 = (a/2)^2 + h^2
(hs)^2 = x^2 + x^2
hs = x * sqrt(2)

Now you have everything you need to calculate x (again, refer to the sketch).

(hs)^2 = 8^2*3 - (a/2)^2
(hs)^2 = 192 - x^2

Since we've already calculated the value of hs, we come to this:

2*x^2 = 192 - x^2

3*x^2 = 192

3*x^2 = 64*3

x^2 = 64

x = 8

Your thinking is correct.