MathDB
Squares and Triangles

Source: Problem #21 2017 AMC 10A, 2017 AMC 12A #19

February 8, 2017
AMCAMC 10AMC 10 A2017 AMC 10AAMC 12 A

Problem Statement

A square with side length xx is inscribed in a right triangle with sides of length 33, 44, and 55 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length yy is inscribed so that one side of the square lies on the hypotenuse of the triangle. What is xy\frac{x}{y}?
<spanclass=′latex−bold′>(A)</span> 1213<spanclass=′latex−bold′>(B)</span> 3537<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> 3735<spanclass=′latex−bold′>(E)</span> 1312<span class='latex-bold'>(A)</span>\ \frac{12}{13}\qquad<span class='latex-bold'>(B)</span>\ \frac{35}{37}\qquad<span class='latex-bold'>(C)</span>\ 1\qquad<span class='latex-bold'>(D)</span>\ \frac{37}{35}\qquad<span class='latex-bold'>(E)</span>\ \frac{13}{12}
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