Use inequality to solve te problem.

Question

One side of a triangle is 2 cm shorter than the base, x.  The other side is 8 cm longer than the base.  What lengths of the base will allow the perimeter of the triangle to be at least 30 cm?

Answer 1

Let the sides be called x, y and b.

1) x = b - 2

2) y = b + 8

3) 30 < or = x + y + b

substitute eqs (1) and (2) into eq(3):

30 < or = (b - 2) + (b + 8) + b

30 < or = 3b + 6

subtract 6 from each side:

24 < or = 3b

divide both sides by 3:

8 < or = b

or

b > or = 8