Question

If the perimeter of a right angled isoscles triangle is $(6+3\sqrt{2})m$, then the area of the triangle will be

• A. $4.5m^2$
• B. $5.4m^2$
• C. $9m^2$
• D. $81m^2$

Answer 1

The correct option is A $4.5m^2$

Let the two equal sides be $x$ m, then the hypotenuse $=x\sqrt{2}$ m
Perimeter of $\Delta =x+x+x\sqrt{2}$

$\Rightarrow x+x+x\sqrt{2}=6+3\sqrt{2}$
$\Rightarrow 2x+x\sqrt{2}=6+3\sqrt{2}$
$\Rightarrow x(2+\sqrt{2})=3(2+\sqrt{2})$

$\Rightarrow x=3$
$\therefore$ Area of the triangle $=\frac{1}{2}\times 3\times 3=4.5m^2$