A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #75 #, what is the length of its longest diagonal?

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Answer 1 · 2016-05-14T13:06:14

Length of its longest diagonal is #28.518#

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 #14# and #15# and area is #75# we have

#14xx15xxsintheta=75# or #sintheta=75/(14xx15)=5/14#

#costheta=sqrt(1-(5/14)^2)=1/14sqrt171=0.934#

Then larger diagonal of parallelogram would be given by

#sqrt(a^2+b^2-2abcos150^@)=sqrt(14^2+15^2+2xx14xx15xx0.934#

= #sqrt(196+225+420xx0.934)=sqrt(421+392.28)#

= #sqrt813.28=28.518#