The sides of a triangle are in the ratio 3 : 4 : 5. State whether the triangle is right-angled or not.

Let the sides of the given triangle are 3x, 4x and 5x units.

For right angled triangle, we have

Square of the longer side = Sum of the square of the other two sides

(5x)² = (3x)² + (4x)²

⇒ 25x² = 9x² + 16x²

⇒ 25x² = 25x²

Hence, the given triangle is a right-angled.

Here, OA = 320 km

AB = 240 km

OB = ?

Clearly, ∆OBA is right angled triangle

OB² = OA² + AB² (By Pythagoras property)

⇒ OB² = 320² + 240²

⇒ OB² = 102400 + 57600

⇒ OB² = 160000

⇒ OB = √160000 = 400 km.

Hence the required shortest distance = 400 km.