Answer:
b=0.5 in
b=2 in
Step-by-step explanation:
we know that
The perimeter of triangle is equal to
[tex]2a+b=15[/tex]
Solve for a
[tex]a=\frac{15-b}{2}[/tex] -----> equation A
Applying the Triangle Inequality Theorem
a+a > b
2a > b -----> inequality B
Verify each case
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
[tex]a=\frac{15-0.5}{2}=7.25\ in[/tex]
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
[tex]a=\frac{15-2}{2}=6.5\ in[/tex]
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
[tex]a=\frac{15-7.9}{2}=3.55\ in[/tex]
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
Answer:
Step-by-step explanation:
We have:
[tex]2a+b=15.7[/tex] subtract b from both sides
[tex]2a+b-b=15.7-b[/tex]
[tex]2a=15.7-b[/tex] divide both sides by 2
[tex]\dfrac{2a}{2}=\dfrac{15.7-b}{2}[/tex]
[tex]a=\dfrac{15.7-b}{2}\qquad\bold{(*)}[/tex]
We know:
[tex]2a>b\qquad\bold{(**)}[/tex]
Subtitute (*) to (**):
[tex]2\!\!\!\!\diagup\cdot\dfrac{15.7-b}{2\!\!\!\!\diagup}>b[/tex]
[tex]15.7-b>b[/tex] add to both sides
[tex]15.7-b+b>b+b[/tex]
[tex]15.7>2b[/tex] divide both sides by 2
[tex]\dfrac{15.7}{2}>\dfrac{2}{b}\\\\7.85>b\to \boxed{b<7.85}\ \text{and}\ \boxed{b>0}[/tex]
Only lengths 0.5in and 2in satisfy this inequality.
