ONE SIDE OF TRIANGLE IS 2CM SHORTER THAN BASE. OTHER SIDE IS 3 CM LONGER THAN BASE.

Question

WHAT LENGTHS OF BASE WILL ALLOW THE PERIMETER TO BE GREATER THAN 19 CM

Answer 1

The perimeter is the distance around a closed plane figure. The perimeter, P, of a triangle is given by the formula P = a + b + c , where a, b and c are the lengths of sides of the triangle.
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Let's assume that length of base is "b", then length of shorter side will be (b-2), and length of longer side will be (b+3) , then P = (b-2) + b + (b+3) > 19
                             3b - 2 + 3 > 19
                             3b + 1 > 19
                                  - 1     - 1   
                              3b > 18 ------> 3b/3 > 18/3 -----------> b > 6

Answer 2

the 3 sides are b, b-2 & b+3. They sum to 3b+1>19 or 3b>18, b>6