A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #60 #, what is the length of its longest diagonal?

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Answer 1 · 2016-09-07T06:17:08

Length of its longest diagonal is #18.92#

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 #12# and #8# and area is #60# we have

#12xx8xxsintheta=60# or #sintheta=60/(12xx8)=5/8#

#costheta=sqrt(1-(5/8)^2)=sqrt(1-25/64)#

= #sqrt(39/64)=1/8sqrt39=6.245/8=0.7806#

Then larger diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcostheta)=sqrt(12^2+8^2+2xx12xx8xx0.7806#

= #sqrt(144+64+192xx0.7806)=sqrt(208+149.8752)#

= #sqrt357.8752=18.92#