Question

In a triangle $ABC$, right angled at $B$, $s-a=3,s-c=2$ then the values of $a$ and $c$ are respectively-

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

Answer 1

The correct option is B $3,4$

Given,

$s-a=3$

$\Rightarrow s=a+3$......(1)

$s-c=2$

$\Rightarrow s=c+2$.......(2)

From (1) and (2)

$a+3=c+2$

$\Rightarrow a-c=-1$......(a)

$2s=a+b+c$

$2s=(s-3)+b+(s-2)$

$\Rightarrow b=5$

Squaring (a), we get,

$(a-c{)}^2=(-1{)}^2$

$a^2+c^2-2ac=1$

$b^2-2ac=1$

$5^2-2ac=1$

$ac=12$

Thus, possibility of a and c will be,

$(1,12),(4,3),(3,4),(6,2),(2,6)and(12,1)$

but only $(3,4)$ satisfies the equation (a)

$\therefore a=3,c=4$