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

Sides $a - d , a , a + d AP$
$( a + d )^{2}= a ^{2}+( a - d )^{2}$
$\Rightarrow a =4 d$
Area $=24 $
$\frac{1}{2} a(a-d) =24$
$ a(a-d) =48 $
$ 12 d^{2} =48 $
$d =2 \,\,(d > 0) $
$ \therefore a =8$
So, sides $6, 8, 10$