SOLUTION: please help me solve this problem..thank you!.. 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 par

Algebra ->  Surface-area -> SOLUTION: please help me solve this problem..thank you!.. 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 par      Log On


   

Question 28999: please help me solve this problem..thank you!..
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.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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