Question

If in triangle ABC, right angled at $B,s-a=3$ and $s-c=2$, then which of the following is correct?

• A. $a=2,c=3$
• B. $a=3,c=4$
• C. $a=4,c=3$
• D. $a=6,c=8$

Answer 1

Answer: (B)

$a=3,c=4$

Given:

$s-a=3\Rightarrow \frac{a+b+c}{2}-a=\frac{b+c-a}{2}=3\Rightarrow b+c-a=\mathrm{6................}\left(1\right)$

Similarly, $s-c=2\Rightarrow a+b-c=\mathrm{4.............}\left(2\right)$

adding $\left(1\right)$&$\left(2\right)$

$a+b-c+b+c-a=10\Rightarrow 2b=10\Rightarrow b=5$

Putting value of b in $\left(1\right)$

$\Rightarrow 5+c-a=6\Rightarrow c-a=1$

Only $B$ is satisfying the given condition

Therefore, Answer is $B$