1979 AMC 12 Problem 1

Attempt Problem 1 of the 1979 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1979 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

If rectangle

ABCD

has area

72

square meters and

E

and

G

are the midpoints of sides

AD

and

CD,

respectively, then the area of rectangle

DEFG

in square meters is

8

9

12

18

24

The two midpoint conditions halve the relevant side lengths

Compare the area scale factor of

DEFG

with that of

ABCD

The side lengths of

DEFG

are one half the corresponding side lengths of

ABCD.

Its area is therefore

(\frac{1}{2})(\frac{1}{2})=\frac{1}{4}

72,

which is

18.

Therefore, the correct answer is D.

Problem 1 in other years