A parallelogram has sides with lengths of #18 # and #4 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

1 Answer
Apr 3, 2016

Length of longest diagonal is #21.56# units.

Explanation:

Area of a parallelogram is given by #axxbxxsintheta#,

where #a# and #b# are two sides of a parallelogram and #theta# is the angle included between them.

As sides are #18# and #4# and area is #36# we have

#18xx4xxsintheta=36# or #sintheta=36/(18xx4)=1/2#

Hence #theta=30^@# and two angles of parallelogram are #30^@# and #150^@#.

Then smaller diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcos30^@)=sqrt(18^2+4^2-2xx18xx4xx(sqrt3/2)#

= #sqrt(324+16-72xxsqrt3)=sqrt215.2923=14.67#

and larger diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcos150^@)=sqrt(18^2+4^2+2xx18xx4xx(sqrt3/2)#

= #sqrt(324+16+72xxsqrt3)=sqrt464.7077=21.56#