1951 AMC 12 Problem 3

Attempt Problem 3 of the 1951 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 1951 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 length of a diagonal of a square is

a+b,

then the area of the square is:

(a+b)^2

\dfrac12(a+b)^2

a^2+b^2

\dfrac12(a^2+b^2)

None of these

Relate the diagonal

d

of a square to its side

s

Since

d=s\sqrt2

, the area

s^2

equals

\frac{d^2}{2}

s

is the side length and

d=a+b

is the diagonal, then

d=s\sqrt2.

Thus

s^2=\frac{d^2}{2}=\frac12(a+b)^2.

Thus, the correct answer is B.

Problem 3 in other years