Shawn has 48 cubes like the one shown. It
She uses all the cubes to fill a box shaped like a larger rectangular prism. There are
no gaps between the cubes.
What is the volume, in cubic feet, of the larger rectangular prism?

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the weight of the object inside the box!

3 4 7 12 19

+1 +3 +5 +6

i would guess 26 because this isnt a sequential pattern or its to short to know