Construct a right triangle of area 8 out of three other right triangles with areas 1, 3 and 4.
Take one triangle with sides 4,2 and sqrt(20). This has area 4.
Take another with sides sqrt(20), sqrt(2) and 3 sqrt(2). This triangle has area 3.
The final triangle has sides 2, sqrt(2) and sqrt(2), and area 1..
Put the first two triangle together at the sqrt(20) side, to get a kite-shape. Put the last triangle next to the area-3 one in such a way that both the sides with length(2) are colinear. This gives the wanted result.
*----*----*
| / \1 /
| 4 / \/
| / 3 /
| / /
| / /
| / /
|/ /
|//
|/
*
solution
