Question 9773
Try this:

Let b cm = the length of the base.
The short side of the triangle would be (b-2) cm.
The long side of the triangle would be (b+3) cm

The perimeter is found by adding the three sides of the triangle, but you want this to be > 19 cm.

So, you can write:

{{{b +(b-2) +(b+3) > 19}}} Solve this inequality for b.

{{{3b +1 > 19}}} Subtract 1 from both sides.

{{{3b > 18}}} Divide both sides by 3.

{{{b > 6}}}

The length of the base would have to be greater than 6 cm in order for the perimeter of this triangle to be greater than 19 cm.

Check:

Try b = 7 cm (since 7 > 6)

7 + (7-2) + (7+3) = 7 + 5 + 10 = 22 and 22 > 19