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

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(52908) (Show Source): You can put this solution on YOUR website!
.


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

         area = ,

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


     From this formula,   =  = 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°) = -   then.



(3)  Now apply the cosine rule


         the length of the longer diagonal =  =  = 70.55 feet.     ANSWER

Solved.

RELATED QUESTIONS
A certain city block is in the form of a parallelogram. Two of its sides measure 82 ft.... (answered by ikleyn)

a certain city block is in the form of a parallelogram. two of its side measures 32ft.... (answered by stanbon)

Please help me with this geometry problem. A certain city block is in the form of a... (answered by josgarithmetic)

The base of a parallelogram is twice its height. If the area of the parallelogram is 72... (answered by ikleyn)

The lengths of the sides of a triangular parcel of land are 300 ft, 350 ft. What is the... (answered by Earlsdon)

Please help me solve this trigo problem. A parcel of land has sides measuring 175 ft.,... (answered by Edwin McCravy)

What is the area of a triangle if the sides are 2.6 ft.,3.4 ft., and 4.1... (answered by priya)

the sides of a rectangle measuring 5 ft and 7 ft . finds its area... (answered by Alan3354)