1960 AMC 12 Problem 21

Attempt Problem 21 of the 1960 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 1960 AMC 12 solutions, or check the answer key.

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

21.

The diagonal of square I is

a+b.

The perimeter of square II with twice the area of I is:

(a+b)^2

\sqrt2(a+b)^2

2(a+b)

\sqrt8(a+b)

4(a+b)

Express the area of square I in terms of its diagonal

Square II’s area is

(a+b)^2,

so find its side length

A square with diagonal

a+b

has area

\frac{(a+b)^2}{2}.

Square II therefore has area

(a+b)^2,

so its side is

a+b

and its perimeter is

4(a+b).

Thus, the correct answer is E.

Problem 21 in other years