Question 29176
the bases of a trapezoid are 100m and 160m, and its altitude equal to 12m. it is to be divided into two equal parts by a line parallel to the base. find the length of the dividing line.
LET A=160 M. THE TOP SIDE...AND ....C=100 M.THE BOTTOM SIDE.
LET THE DIVIDING SIDE BE B M.
AREA OF TRAPEZIUM = (1/2)(SUM OF PARALLEL SIDES)*ALTITUDE
SINCE TRAPEZEUM IS DIVIDED IN TO 2 EQUAL PARTS,WE HAVE
0.5*(160+B)*HTOP=0.5(B+100)*HBOT
SINCE HEIGHT IS PROPORTIONAL TO DIFFERENCE IN PARALLEL SIDES ,WE HAVE
HTOP=K*(160-B)
HBOT=K*(B-100)
HENCE
0.5*(160+B)*K(160-B)=0.5(B+100)*K*(B-100)
160^2-B^2=B^2-100^2
B^2=(160^2+100^2)/2=35600/2=17800
B=SQUARE ROOT OF (17800)=133.4

FIGURE IS GIVEN BELOW....
{{{drawing( 800, 800,-40,140,-10,20,red( line( 0, 0, 100,0 ) ),locate( 0, 0, A ),red( line( 100, 0, 130,12 ) ),locate( 100,0, B ),red( line( 130,12, -30,12 ) ),locate( 130, 12, C ),red( line( -30, 12, 0,0 ) ),locate( -30, 12, D ),green( line( -16.5,6.6, 116.5,6.6 ) ),locate(-16.5,6.6,E),locate(116.5,6.6,F ) )}}}