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The number of values of $b$ for which there is an isosceles triangle with sides of length $b+5,3 b-2$ and $6-b$ is
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Verified Answer
The correct answer is:
$2$
Case (I)
$b+5=3 b-2$
$\Rightarrow b=\frac{7}{2}$
So sides are $\frac{17}{2}, \frac{17}{2}, \frac{5}{2}$
Case (II)
$b+5=6-b=b=\frac{1}{2}$
Sides $\frac{11}{2}, \frac{-1}{2}, \frac{11}{2}$ Not possible
Case (III)
$3 \mathrm{~b}-2=6-\mathrm{b}$
$4 \mathrm{~b}=8$
$\mathrm{~b}=2$
$7,4,4$
two cases are possible.
$b+5=3 b-2$
$\Rightarrow b=\frac{7}{2}$
So sides are $\frac{17}{2}, \frac{17}{2}, \frac{5}{2}$
Case (II)
$b+5=6-b=b=\frac{1}{2}$
Sides $\frac{11}{2}, \frac{-1}{2}, \frac{11}{2}$ Not possible
Case (III)
$3 \mathrm{~b}-2=6-\mathrm{b}$
$4 \mathrm{~b}=8$
$\mathrm{~b}=2$
$7,4,4$
two cases are possible.
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