SOLUTION: A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft. and 25 ft. If the area of the land in the block is 1,467 sq. ft., what is the length of the

Question 1150859: A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft. and 25 ft. If the area of the land in the block is 1,467 sq. ft., what is the length of the shorter diagonal?

Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.


Use the formula  S =   for the area of a parallelogram,

where "a" and "b" are any two adjacent side lengths and   is the concluded angle between them.


From the formula,


     =  = 0.71561.


Then   =  =  = 0.6985.


     Notice that for the shorter diagonal, we choose the positive sign of  .


Now apply the cosine law.


The shorter diagonal is  .


Substitute the data and calculate the numerical value on your own.

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