**Answer:**

b=0.5 in

b=2 in

**Step-by-step explanation:**

we know that

The perimeter of triangle is equal to

Solve for a

-----> equation A

Applying the Triangle Inequality Theorem

a+a > b

2a > b -----> inequality B

**<u>Verify each case</u>**

**case 1)** b=-2 in

This value not make sense, the length side cannot be a negative number

**case 2)** b=0 in

This value not make sense

**case 3)** b=0.5 in

substitute the value of b in the equation A and solve for a

substitute the values of b and a in the inequality B

2a > b

2(7.25) > 0.5

14.50 > 0.5 -----> is true

therefore

b=0.5 in make sense for possible values of b

**case 4)** b=2 in

substitute the value of b in the equation A and solve for a

substitute the values of b and a in the inequality B

2a > b

2(6.5) > 2

13 > 2 -----> is true

therefore

b=2 in make sense for possible values of b

**case 5)** b=7.9 in

substitute the value of b in the equation A and solve for a

substitute the values of b and a in the inequality B

2a > b

2(3.55) >7.9

7.1 > 7.9 -----> is not true

therefore

b=7.9 in not make sense for possible values of b