If RE*ER= AREA evaluate the AREA .

Please evaluate using pencil and paper only.

We have 1001a+100r+10e on RHS.

Move the r and e factors to LHS: (10r+e)*(10e+r)-100r-10x; (10(e-1)+r)(10r+e) = 1001a.

1001=7*11*13

Assume 11 divides (10r+e); then r=e. So 11 divides (10(e-1)+r) and r=(e-1). If 13*7 divides (10r+e) then e=1, which is impossible since r would then equal both 0 and 9. So (10(e-1)+r)=77 and e=8,r=7. Now we have 87*78 = 6786 and a=6.

QED

Posted by broll on 2011-04-09 07:23:23