Question

The hypotenuse of a right triangle is 10cm and radius of thE inscribed circle is 1 cm. The perimeter of the triangle is:

• A. 15 cm
• B. 22 cm
• C. 24 cm
• D. 18 cm

Answer 1

Answer: (B)

22 cm

$r=\frac{\Delta }{s}$
$1=\frac{a.b}{2s}$
$a+b+10=a.b$
$a+b=ab-10$
$(a+b{)}^2=(ab-10{)}^2$
$a^2+b^2+2ab=a^2{b}^2-20ab+100$
$\because a^2+b^2=100$
$\Rightarrow 2ab=a^2{b}^2-20ab$
$\Rightarrow a^2{b}^2-22ab=0$
$\Rightarrow ab(ab-22)=0$
$\Rightarrow ab=22$ $\because ab\ne 0$
$\therefore$ perimeter $=a+b+10=ab=22$