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

Step-by-step solution

Let three sides of triangle be: a - d , a , a + d . Where, d > 0 , a > 0 . ⇒ length of smallest side = a - d units Now, ( a + d ) 2 = a 2 + ( a − d ) 2 ⇒ a a - 4 d = 0 ∴ a = 4 d .....(i) (As a = 0 is rejected) Also, 1 2 a . a - d = 24 ⇒ a a - d = 48 .....(ii) ∴ From (i) and (ii), we get a = 8 , d = 2 Hence, length of smallest side is a - d = 8 - 2 = 6 units