A parallelogram has sides with lengths of #12 # and #6 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

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Answer 1 · 2016-04-30T08:47:00

Longest diagonal of the parallelogram is #16.95#

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

Hence, in the given instance #12xx6xxsintheta=48#

or #sintheta=48/(12xx6)=2/3#

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

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

As #costheta=sqrt(1-(2/3^2)=sqrt(1-4/9)=sqrt5/9=1/3sqrt5#

Hence, #L=sqrt(12^2+6^2+2xx12xx6xx1/3sqrt5)#

= #sqrt(144+36+48sqrt5=sqrt(180+48xx2.236)=sqrt287.328=16.95#