Question

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

Answer 1

Let the sides are a - d, a and a + d. Then,
a (a - d) = 48 sq. units (from eqn. of area of triangle)
and $(a-d{)}^2+a^2=(a+d{)}^2$ . . .(Pythagoras)
$\Rightarrow a^2-2ad+d^2+a^2=a^2+2ad+d^2$
$\Rightarrow a^2=4ad$
$\Rightarrow a=4d$
$Thus,a=8,d=2$
$Hence,a-d=6units$