2024/039) The sides of a right angled triangle are in AP and area of 24. What are the length of sides

 Let the sides be a, a-d and a + d

we have $(a-d)^2 + a^2 = (a-d)^2$

or $a^2-2ad + d^2 + a^2 = a^2 + 2ad + d^2$

or $a^2 -4ad=0$

 or $a(a-4d)=0$

so $a=4d$

area of the $\triangle$  is $\frac{a(a-d)}{2} = 24$

or $\frac{4d * 3d}{2} = 24$

or d= 2 and hence sides are 6,8, 12