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 ?

Sides of the triangle are $\mathrm{a}-\mathrm{d},\mathrm{a},\mathrm{a}+\mathrm{d}(\mathrm{a},\mathrm{d}>0,\mathrm{d}<\mathrm{a}){\mathrm{a}}^2+(\mathrm{a}-\mathrm{d}{)}^2=(\mathrm{a}+\mathrm{d}{)}^2\Rightarrow {\mathrm{a}}^2=4\mathrm{ad}\Rightarrow \mathrm{a}=4\mathrm{d}$
$\Rightarrow$sides are 3d, 4d, 5d
Area$=24\Rightarrow \frac{1}{2}\left(3\mathrm{d}\right)\left(4\mathrm{d}\right)=24\Rightarrow {\mathrm{d}}^2=4\Rightarrow \mathrm{d}=2$
smallest side is 3d=6