A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

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Answer 1 · 2016-05-12T09:12:22

Longest diagonal of parallelogram is #22.76#

Area of a parallelogram is given by #axxbxxsintheta#, where #a# and #b# are two sides of parallelogram and #theta# is angle included between them.

Hence #15xx8xxsintheta=36# or #sintheta=36/(15xx8)=36/120=0.3#

Therefore #costheta=sqrt(1-0.3^2)=sqrt(0.91)=0.954#

The longest diagonal would be given by cosine formula and hence it is

#sqrt(15^2+8^2+2xx15xx8xx0.954#

= #sqrt(225+64+228.96)#

= #sqrt517.96=22.76#