Problem
Cut A's extra 10 cm off — the bars match, leaving 80 cm.
The 90 cm total is really two shorter-bar lengths plus the 10 cm piece joined together. Taking that 10 cm back off (subtracting undoes the adding) leaves exactly two shorter-bar lengths, 80 cm.
Draw A Diagram2.MD.B.5Cutting the 10 cm extra piece off the 90 cm total drops it to 80 cm, and that 80 cm is the shorter bar counted twice.
The 90 cm total is the two bars laid end to end, and the longer bar is the shorter bar plus the 10 cm piece, so the total is really two shorter-bar lengths and one 10 cm piece.
The two bars are joined end to end with no gap and no overlap, so their two lengths add up to the whole 90 cm.
The longer bar runs alongside the shorter bar and then keeps going for the 10 cm piece, so the longer bar is the shorter-bar length and the piece joined together.
The 10 cm piece is the one extra part added on top of the two shorter-bar lengths, so subtracting it undoes that adding and leaves exactly the two shorter-bar lengths, which is 80 cm.
80 cm is two equal bars — halve it to get B, 40 cm.
The 80 cm left after removing the extra piece equals two copies of the shorter bar B joined together. Splitting it evenly in two gives one copy — the length of B.
Identify Subproblems2.MD.B.5Add the 10 cm piece back to B's 40 cm — A is 50 cm.
The longer bar A is just B with the 10 cm piece that was removed put back on. So adding 10 cm to B's length gives A's length.
Identify Subproblems2.MD.B.5Remove the extra piece, halve what's left, then add it back to find both lengths.