SOLUTION: The perimeter of a triangle measures 82 feet. All three sides are of different lengths. The longest side is 12 feet less than three times the length of the smallest side. The middl

Algebra ->  Triangles -> SOLUTION: The perimeter of a triangle measures 82 feet. All three sides are of different lengths. The longest side is 12 feet less than three times the length of the smallest side. The middl      Log On


   

Question 954270: The perimeter of a triangle measures 82 feet. All three sides are of different lengths. The longest side is 12 feet less than three times the length of the smallest side. The middle length side is 26 feet Find the length of the Smallest and longest side. Please show all work if possible.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a,b,and c=sides of triangle
a=smallest side; b=26 feet;c=3a-12 feet; p=perimeter
p=a+b+c
82 feet=a+26feet+c Subtract 26 from each side.
56 feet=a+c Substitute for c.
56 feet=a+3a-12 feet Add 12 feet to each side.
68 feet=4a Divide each side by 4.
17 feet=a ANSWER 1: The shortest side is 17 feet.
c=3a-12 feet=3(17 feet)-12 feet=51 feet-12 feet=39 feet ANSWER 2: The longest side is 37 feet.
CHECK:
a+b+c=82 feet
17 ft+26 ft+39 ft=82 ft
82 ft=82 ft