Problem
1957 AHSME Problem 37
In right triangle ABC, BC = 5, AC = 12, and AM = x; \overline{MN} \perp \overline{AC}, \overline{NP} \perp \overline{BC}; N is on AB. If y = MN + NP, one-half the perimeter of rectangle MCPN, then:
![[asy] defaultpen(linewidth(.8pt)); unitsize(2cm); pair A = origin; pair M = (1,0); pair C = (2,0); pair P = (2,0.5); pair B = (2,1); pair Q = (1,0.5); draw(A--B--C--cycle); draw(M--Q--P); label("$A$",A,SW); label("$M$",M,S); label("$C$",C,SE); label("$P$",P,E); label("$B$",B,NE); label("$N$",Q,NW);[/asy]](/static/aops/c29954e48d094adb9f8ad33c142a06c2b1cba5a6.png)
\begin{array}{l} \textbf{(A)}\ y = \frac {1}{2}(5 + 12) \qquad \textbf{(B)}\ y = \frac {5x}{12} + \frac {12}{5}\qquad \textbf{(C)}\ y =\frac{144-7x}{12}\qquad \\ \textbf{(D)}\ y = 12\qquad \qquad\quad\,\, \textbf{(E)}\ y = \frac {5x}{12} + 6 \end{array}
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