Question

In triangle $ABC,$ right angle at $B$ if $s-a=3,s-c=2$ then $a,c$ are

• A. $1,4$
• B. $3,4$
• C. $2,4$
• D. None of these

Answer 1

The correct option is B $3,4$

Given,

$s-a=3$

$\frac{a+b+c-2a}{2}=3$

$b+c-a=6$

and $s-c=2$

$\frac{a+b+c}{2}-c=2$

$a+b-c=4$

Adding them, we get

$2b=10$

$\Rightarrow b=5$

$c-a=b-5=1$

Also, $a^2+c^2=b^2=5^2=25$

$a^2+(1+a{)}^2=25$

$2a^2+2a-24=0$

$\Rightarrow a^2+a-12=0$

$\Rightarrow (a-3)(a+4)=0$

$\Rightarrow a=3$

Hence $c=1+a=1+3=4$.