Question

The perimeter of a triangle is $100$ cm and its sides are the ratio $1:2:3$. The area of the triangle $\left({\text{in cm}}^2\right)$ is

• A. $100\sqrt{3}$
• B. $100\sqrt{15}$
• C. $100\sqrt{5}$
• D. $100\sqrt{7}$

Answer 1

The correct option is B $100\sqrt{15}$

Sides of the triangle are 20,40,40 which is an isosceles triangle
Area of isosceles triangle $=\frac{1}{4}.b.\sqrt{4a^2-b^2}$
where 'b' is the base and 'a' being equal side
Here b = 20
$\therefore$ Area $=\frac{1}{4}\times 20\times \sqrt{4\times 40\times 40-20\times 20}$
$=100\sqrt{15}$