Question

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to

• A. 8.64
• B. 12
• C. 6
• D. 10.28

Answer 1

The correct option is A 8.64

Le the lengths of the triangle be, $3x,4x,5x$
Square of largest side = $25x^2$
Sum of square of other sides = $(3x{)}^2+(4x{)}^2=25x^2$
Since, the square of largest side is equal to the sum of square of other sides, hence, it is a right angled triangle.
For a right angled triangle the diameter of the circumcircle is equal to the hypotenuse of the triangle.
hence, $5x=6$ or $x=\frac{6}{5}$
Now, two perpendicular sides are then, $\frac{18}{5},\frac{24}{5}$
Area = $\frac{1}{2}\times \frac{18}{5}\times \frac{24}{5}$ = $8.64$