Correct Answer - Option 3 : 56 units
Given:
Ratio of sides of triangle is x : (x - 1) : (x - 18)
Formula:
Pythagoras theorem,
(diagonal)2 = (side1)2 + (side2)2
Calculation:
Let sides of right angled triangle be ax, a(x - 1), a(x - 18) respectively.
(ax)2 = [a(x - 1)]2 + [a(x - 18)]2
⇒ x2 = x2 - 2x + 1 + x2 - 36x + 324
⇒ x2 - 38x + 325 = 0
⇒ x = 25 or x = -13
Sides of right angled triangle = 25, 24 and 7
∴ Perimeter of right angled triangle = 25 + 24 + 7 = 56 units
