1975 AMC 12 Problem 4

Attempt Problem 4 of the 1975 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 1975 AMC 12 solutions, or check the answer key.

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

If the side of one square is the diagonal of a second square, what is the ratio of the area of the first square to the area of the second?

2

\sqrt2

\frac12

2\sqrt2

4

If the first side is

s,

then the second square has diagonal

s

A square with diagonal

s

has area

\frac{s^2}{2}

Let the first square have side

s.

The second has diagonal

s,

so its side is

\frac{s}{\sqrt2}

and its area is

\frac{s^2}{2}.

The ratio is

\frac{s^2}{\frac{s^2}{2}}=2.

Therefore, the correct answer is A.

Problem 4 in other years