SOLUTION: The shortest side of a triangle is one half the length of the middle side, plus 2 cm. The longest side of the triangle is one and one-half times the length of the middle side, les

Algebra ->  Pythagorean-theorem -> SOLUTION: The shortest side of a triangle is one half the length of the middle side, plus 2 cm. The longest side of the triangle is one and one-half times the length of the middle side, les      Log On


   

Question 267116: The shortest side of a triangle is one half the length of the middle side, plus 2 cm. The longest side of the triangle is one and one-half times the length of the middle side, less 2 cm. The perimeter of the triangle is 60 cm. How long are each of the sides?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let us suppose that shortest side = x cm, middle side = y cm and longest side = z cm.
The shortest side of a triangle is one half the length of the middle side, plus 2 cm. This means x+=+%281%2F2%29%2Ay+%2B+2 _____ (1)
The longest side of the triangle is one and one-half times the length of the middle side, less 2 cm. This means, z+=+%283%2F2%29%2Ay+-+2 ______ (2)

Also given, perimeter = 60 cm i.e. x+%2B+y+%2B+z+=+60 _______ (3)

Substituting for x and z from (1) and (2) respectively into (3), we have
%281%2F2%29%2Ay+%2B+2+%2B+y+%2B+%283%2F2%29%2Ay+-+2+=+60
%281%2F2%29%2Ay+%2B+y+%2B+%283%2F2%29%2Ay+=+60
3%2Ay+=+60
y=+60%2F3=20

Hence, x+=+%281%2F2%29%2A20+%2B+2+=+12 and z+=+%283%2F2%29%2A20+-+2+=+28

The sides of the triangle are: 12 cm, 20 cm and 28 cm.