ONE SIDE OF A TRIANGLE IS 3 CM SHORTER THAN BASE. OTHER SIDE IS 4 CM LONGER THAN BASE.

Question

WHAT LENGTHS OF BASE WILL ALLOW PERIMETER TO BE GREATER THAN 28 CM

Answer 1

First, we are going to label our variables:

B = Base of triangle

S1 = The first side of the triangle

S2 = The second side of the triangle

Since the first side of the triangle is 3 cm shorter than the base, we can say that:

S1 = B - 3

Since the second side of the triangle is 4 cm shorter than the base, we can say that:

S2 = B - 4

The perimeter of a triangle is the sum of the lengths of the side.  For the perimeter to be greater than 28, we would state:

B + S1 + S2 > 28

By substituting the information relating the base to the two sides into the perimeter formula, we get:

B + (B - 3) + (B - 4) > 28

B + B - 3 + B - 4 > 28                        Associative property of addition

3B - 7 > 28                                       Simplify

3B - 7 + 7 > 28 + 7                           Add 7 to each side

3B > 35                                            Simplify

3B/3 > 35/3                                      Divide each side by 3

B > 35/3                                           Simplify

Any length of base bigger than 35/3 will produce a perimeter greater than 28 cm.  If you need integers, than any length of 12 cm or longer will work.