SOLUTION: A certain city block is in the form of a parallelogram. Two of its sides measure 32 ft and 41 ft. If the area of the land in the block is 656 square feet, what is the length of its

Algebra ->  Parallelograms -> SOLUTION: A certain city block is in the form of a parallelogram. Two of its sides measure 32 ft and 41 ft. If the area of the land in the block is 656 square feet, what is the length of its      Log On


   

Question 1161587: A certain city block is in the form of a parallelogram. Two of its sides measure 32 ft and 41 ft. If the area of the land in the block is 656 square feet, what is the length of its longer diagonal?
Answer by ikleyn(52899) About Me  (Show Source):
You can put this solution on YOUR website!
.

(1)  Use the formula for the area of the partallelogram

         area = a%2Ab%2Asin%28alpha%29,

     where "a" and "b" are any two adjacent sides of the parallelogram and  alpha  is the angle concluded between them. 


     From this formula,  sin%28alpha%29 = 656%2F%2832%2A41%29 = 0.5.



(2)  Hence, the acute angle of the parallelogram is 30°,  and the obtuse angle is 150°.

     The cosine of the obtuse angle is  cos(150°) = - sqrt%283%29%2F2  then.



(3)  Now apply the cosine rule


         the length of the longer diagonal = sqrt%2832%5E2+%2B+41%5E2+%2B+2%2A32%2A41%2A%28sqrt%283%29%2F2%29%29 = sqrt%284977.451%29 = 70.55 feet.     ANSWER

Solved.