# 1975 AHSME Problems/Problem 4

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## Problem

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? $\textbf{(A)}\ 2 \qquad \textbf{(B)}\ \sqrt2 \qquad \textbf{(C)}\ 1/2 \qquad \textbf{(D)}\ 2\sqrt2 \qquad \textbf{(E)}\ 4$

## Solution

Solution by e_power_pi_times_i

Denote the side of one square as $s$. Then the diagonal of the second square is $s$, so the side of the second square is $\dfrac{s\sqrt{2}}{2}$. The area of the second square is $\dfrac{1}{2}s^2$, so the ratio of the areas is $\dfrac{s^2}{\dfrac{1}{2}s^2} = \boxed{\textbf{(A) } 2}$.

## See Also

 1975 AHSME (Problems • Answer Key • Resources) Preceded byProblem 3 Followed byProblem 5 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 All AHSME Problems and Solutions

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