SOLUTION: The perimeter of a triangle is 65 centimeters. The longest side is 7 centimeters longer than the shortest side. The midlength side is 4 centimeters longer than the shortest side. F

Algebra ->  Triangles -> SOLUTION: The perimeter of a triangle is 65 centimeters. The longest side is 7 centimeters longer than the shortest side. The midlength side is 4 centimeters longer than the shortest side. F      Log On


   

Question 951514: The perimeter of a triangle is 65 centimeters. The longest side is 7 centimeters longer than the shortest side. The midlength side is 4 centimeters longer than the shortest side. Find the length of the longest side.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
a=shortest side; b=midlength side=a+4cm;c=longest side=a+7cm; p=perimeter=a+b+c=65cm
p=a+b+c Subistute for b and c.
65cm=a+(a+4cm)+(a+7cm)
65cm=3a+11cm Subtract 11 cm from each side.
54cm=3a Divide each sid by 3.
18cm=a
c=a+7cm=18cm+7cm=25cm ANSWER: The longest side is 25 cm.
CHECK:
b=a+4cm
b=18cm+4cm=22cm
p=a+b+c
65cm=18cm+22cm+25cm
65cm=65cm