In the #DeltaABC# below, #M# and #N# are midpoints of #BC# and #AB# respectively, #m/_A=90^@#. Find #x,y# and #z#?

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1 Answer
Jul 6, 2016

#x=9.67#, #y=2# and #z=36#

Explanation:

As M is the midpoint of BC, we have

#36=40-2y# and transposing similar terms we get

#2y=40-36=4#. Hence, #y=2#.

As #M# is the midpoint of #BC# and it joins mid point of #AB# at the base at #N#, then #MN# is half of #AC=36# and hence

#3x-11=36/2=18# i.e.

#3x=18+11=29# and #x=29/3=9.67#.

As #MN# joins mid points of #AB# and #BC#, it too is perpendicular to #AB# (as #MN#||#AC#) and #DeltasMNB# and #AMN# are congruent (SAS) and hence #BM=AM#.

Hence, #z=36#.