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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