AMC 10 · 2021 · #2
Grade 3 geometry-2dPick an answer.
The missing piece of information — which side got shortened — has only two candidates, so Tool #2 (Make a Systematic List) writes down both cards and both areas in a two-row table instead of guessing. Tool #3 (Eliminate Possibilities) then uses the one number the problem hands over, the area 18, to cross off the row that does not fit; the surviving row identifies which side was actually cut, and the crossed-off row is exactly the card the question asks about. Tool #1 (Draw a Diagram) keeps the two cuts straight: sketching the rectangle shows that trimming a side removes a thin strip along one edge, which makes it obvious the two cuts are not interchangeable.
See the card and its two cuts
See the card and its two cuts.
A rectangle has just two different side lengths, so shortening "a side" can only mean one of two things.
A rectangle has just two different side lengths, so shortening a side can only mean one of two things.
▸ Why?
The two cases never overlap, so checking both covers every reading of the story.
▸ Why?
The card is exactly its two side lengths, so nothing else can be what was shortened.
List both resulting cards
List both resulting cards.
With only two possibilities, computing both is faster and safer than trying to reason out which one is meant.
3.MD.C.7Make A Systematic ListLet the 18 pick the row
The given 18 picks the row.
The given area is not decoration — it is the clue that tells you which of the two cuts the story is describing.
3.OA.D.8Eliminate PossibilitiesRead off the other row
Reading the other row gives 20.
Once you know which cut was described, the answer is the row of the table you did not use.
3.MD.C.7Make A Systematic ListWhen a problem hides which side changed, try both — the number it hands you tells you which case really happened, and the case you crossed off is usually what it asks for next.
- See the card and its two cuts
- List both resulting cards
- Let the 18 pick the row
- Read off the other row