Question

The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$, then what is the length of its smallest side?

Answer 1

Let the sides of the triangle be $a-d,a,a+d$
$a^2+(a-d{)}^2=(a+d{)}^2\Rightarrow a(a-4d)=0\because a\ne 0,\Rightarrow a=4d\text{Sides are}3d,4d,5d\text{Given, area}=24\frac{1}{2}\times 3d\times 4d=24\Rightarrow d=2\Rightarrow \text{Sides are}6,8,10\therefore \text{Smallest side is}6.$