A parallelogram has sides with lengths of #18 # and #5 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

1 Answer
Apr 30, 2016

Longest diagonal of the parallelogram is #20.55#

Explanation:

Area of a parallelogram whose sides are #a# and #b# and included angle #theta# is #axxbxxsintheta#

Hence, in the given instance #18xx5xxsintheta=36#

or #sintheta=36/(18xx5)=0.40#

Longest diagonal #L# of the parallelogram will be given by cosine formula

#L=sqrt(a^2+b^2+2abcostheta)#

As #costheta=sqrt(1-0.4^2)=sqrt0.84#

Hence, #L=sqrt(18^2+5^2+2xx18xx5xxsqrt0.84)#

= #sqrt(324+25+180xx0.9165)=sqrt(349+73.32)=sqrt422.32=20.55#

Smaller diagonal would be #S=sqrt(18^2+5^2-2xx18xx5xxsqrt0.84)=sqrt(349-73.32)=16.60#