Question

In $\Delta$ $ABC,B={90}^0$ and $s-a=3$ and $s-c=2$ then $(a,c)=$

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

Answer 1

The correct option is B (3, 4)

$sin\frac{B}{2}=\sqrt{\frac{(5-a)(5-c)}{ac}}$

$\frac{1}{2}=\frac{3\times 2}{ac}$

$ac=12$

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

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

$b+c-a=6$

$b+a-c=4$

$2b=10$

$b=5$

$c-a=1$

$b^2=c^2+a^2$

$c=a+1$

$a^2+a-12=0$

$a=3,a=-4$

$a>0$

$\therefore a=3$

$c=4$.