There is only one solution that will enable us to retain the larger of the two pieces with as little as possible cut from it. 
Fig. 1 in the following diagram shows how the smaller piece is to be cut, and Fig. 2 how we should dissect the larger piece, while in Fig. 3 we have the new square 10 × 10 formed by the four pieces with all the chequers properly matched. 
It will be seen that the piece D contains fifty-two chequers, and this is the largest piece that it is possible to preserve under the conditions.