1975 AHSME Problems/Problem 4
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?
Solution by e_power_pi_times_i
Denote the side of one square as . Then the diagonal of the second square is , so the side of the second square is . The area of the second square is , so the ratio of the areas is .