2021 Fall AMC 12A Problem 2

Problem 2 of 25EasierGeometry

Menkara has a

4 \times 6

index card. If she shortens the length of one side of this card by

1

inch, the card would have area

18

square inches. What would the area of the card be in square inches if instead she shortens the length of the other side by

1

inch?

Show solution

Solution

The original card is

4 \times 6.

Shortening a side by

1

inch gives area

18,

which requires

3 \times 6 = 18,

so the reduced side was the

4

-inch side. Shortening the other side by

1

inch instead gives

4 \times 5 = 20

square inches. Thus, the correct answer is E.