A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #45 #, what is the length of its longest diagonal?

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Answer 1 · 2018-02-17T17:35:43

the longest diagonal is26.4

Area of parallelogram = base . altitude

Area = #45#
base=#15#
altitude = #12sintheta#

#45=15xx12sintheta#

#45=180sintheta#

#sintheta=45/180#
#sintheta=1/4#

Further, the longest diagonal is given by the vectorial sum of the two adjacent sides

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

#a=15, b=12, costheta=sqrt(1-(1/4)^2)=sqrt15/2#
#=sqrt(15^2+12^2+2xx15xx12xxsqrt15/2#

#=sqrt(225+144+180sqrt15#
#sqrt(369+180sqrt15)=26.4#
the longest diagonal is26.4