The shaded area in the diagram below shows the cross section of a square pyramid intersected by a plane parallel to the base. The pyramids edges are all 15 cm long.

What is the perimeter of the shaded area?

Question

The shaded area in the diagram below shows the cross section of a square pyramid intersected by a plane parallel to the base. The pyramids edges are all 15 cm long.
 

 
What is the perimeter of the shaded area?

anonymous · Answer

attachment

tkhunny · Answer

Hint: Similar Triangles
Hint: Similar Pyramids
Hint: Similar Squares

anonymous · Answer

So do I have to find a ratio?

tkhunny · Answer

No, not "a" ratio, "the" ratio, but you do have the idea.

anonymous · Answer

When I do that I get 40 as my answer

anonymous · Answer

I set it up as 9/15=6/X   Which gives me X equaling 10. Which I use to get the perimeter

anonymous · Answer

So what am I doing wrong

tkhunny · Answer

9 is nothing.  It is not the edge of a triangle.
x is not defined.

What were you trying to do?

anonymous · Answer

I was trying to establish some sort of similarity ratio between the similar sides

anonymous · Answer

i think i understand is the answer 24

tkhunny · Answer

Good call.

The ratio is $\dfrac{BigSide}{LittleSide} = \dfrac{9+6}{6} = \dfrac{15}{x} = \dfrac{BigBase}{LittleBase}$.

Labels and documentation can go a long way.  :-)

anonymous · Answer

Thanks so much. it really helped to talk it through.