Question 57824
construct a paralellogram ABCD in which BC=5.5cm, CD=2.5cm and angle ABC=60 degrees. Measure AC and BD
IN A PARALELOGRAM OPPOSITE SIDES ARE EQUAL.
HENCE AB=CD=2.5....BC=DA=5.5
DRAW BC = 5.5.
WITH B AS CENTRE DRAW AN ARC OF RADIUS = AB = 2.5.
AT B DRAW A LINE BX MAKING ANGLE OF 60 DEGREES WITH BC..THAT IS ANGLE XBC=60
LET THE ARC CUT BX AT A.
WITH A AS CENTRE AND RADIUS EQUAL TO AD=5.5 DRAW AN ARC.
WITH C AS CENTRE AND RADIUS EQUAL TO CD=2.5 DRAW AN ARC.
LET THE 2 ARCS CUT AT D.
JOIN CD AND DA
ABCD IS THE REQUIRED PARALLELOGRAM.
AC^2=AB^2+BC^2-2*AB*BC*COS(60) =  22.75
AC=4.77=4.8
BD=AC^2+CB^2-2*AC*CB*COS(120)= 50.25
BD=7.09=7.1
{{{drawing(600,600,-10,10,-10,10,red(line(0,0,5.5,0),line(5.5,0,6.75,2.17),line(0,0,1.25,2.17),line(1.25,2.17,6.75,2.17)),
locate(0,0,B),locate(5.5,0,C),locate(6.75,2.17,D),locate(1.25,2.17,A))}}}