MathDB

11

Part of 1986 AMC 12/AHSME

Problems(1)

Line length

Source: AHSME 1986 problem 11

9/30/2011
In △ABC\triangle ABC, AB=13AB = 13, BC=14BC = 14 and CA=15CA = 15. Also, MM is the midpoint of side ABAB and HH is the foot of the altitude from AA to BCBC. The length of HMHM is
[asy] size(200); defaultpen(linewidth(0.7)+fontsize(10)); pair H=origin, A=(0,6), B=(-4,0), C=(5,0), M=B+3.6*dir(B--A); draw(B--C--A--B^^M--H--A^^rightanglemark(A,H,C)); label("AA", A, NE); label("BB", B, W); label("CC", C, E); label("HH", H, S); label("MM", M, dir(M)); [/asy]
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 6.5<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 7.5<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 6.5\qquad<span class='latex-bold'>(C)</span>\ 7\qquad<span class='latex-bold'>(D)</span>\ 7.5\qquad<span class='latex-bold'>(E)</span>\ 8
AMC