Let's consider the shortest side of the triangle to be [tex]s[/tex]. We can say then that the medium side is [tex]s + 8[/tex], since it is 8cm longer than the shortest side [tex]s[/tex]. We can also say that the longest side is [tex]2s + 2[/tex], since it is 2cm longer than twice the shortest side [tex]s[/tex].
The perimeter of a shape is the sum of the lengths of its sides. Using this, we can say that the perimeter of the triangle is:
[tex]s + (s + 8) + (2s + 2)[/tex]
By combining like terms, we can simplify the expression:
[tex]4s + 10[/tex]
The problem stated that the perimeter was 142 cm, so we can set the expression we just found equal to 142 and solve:
[tex]4s + 10 = 142[/tex]
[tex]4s = 132[/tex]
[tex]s = 33[/tex]
We now know the length of the shortest side, which is 33 cm. By substituting the value we just found for [tex]s[/tex] into our other side lengths, we can find them as well.
The side lengths of our triangle are 33 cm, 41 cm, and 68 cm.
