SOLUTION: A pie-shaped (triangular) lake-front lot has a perimeter of 1500 feet. One side is 400 feet longer than the shortest side, while the third side is 500 feet longer than the shortest

Algebra ->  Equations -> SOLUTION: A pie-shaped (triangular) lake-front lot has a perimeter of 1500 feet. One side is 400 feet longer than the shortest side, while the third side is 500 feet longer than the shortest      Log On


   

Question 1162624: A pie-shaped (triangular) lake-front lot has a perimeter of 1500 feet. One side is 400 feet longer than the shortest side, while the third side is 500 feet longer than the shortest side. Find the lengths of all three sides.
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, you have this equation


    x + (x+400) + (x + 500) = 1500 feet,


where x is the length of the shortest side.


From this equation


    x = %281500+-+400-500%29%2F3 = 200  feet.


Thus the sides are  200 ft, 200+400 = 600 ft  and  200+500 = 700 ft.


The triangle inequalities are hold, so such a triangle does exist.


ANSWER.  The sides are  200 ft,  600 ft  and  700 ft.

Solved.