1960 AHSME Problems/Problem 21

Revision as of 20:24, 10 May 2018 by Rockmanex3 (talk | contribs) (Solution to Problem 21)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

The diagonal of square $I$ is $a+b$. The perimeter of square $II$ with twice the area of $I$ is:

$\textbf{(A)}\ (a+b)^2\qquad \textbf{(B)}\ \sqrt{2}(a+b)^2\qquad \textbf{(C)}\ 2(a+b)\qquad \textbf{(D)}\ \sqrt{8}(a+b) \qquad \textbf{(E)}\ 4(a+b)$

Solution

Since the diagonal of square $I$ is $a+b$ units long, the side length of square $I$ is $\frac{a+b}{\sqrt{2}}$, so the area of square $I$ is $\frac{(a+b)^2}{2}$.

The area of square $II$ is twice as much as the area of square $I$, so the area of square $II$ is $(a+b)^2$. That means the side length of square $II$ is $a+b$, so the perimeter of square $II$ is $4(a+b)$, or answer choice $\boxed{\textbf{(E)}}$.

See Also

1960 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
All AHSME Problems and Solutions
Invalid username
Login to AoPS