Question

The hypotenuse of a right-angled triangle is 20 meters. If the difference between the lengths of the other sides be 4 meters, find the other sides. 

Answer 1

Let one side of the right-angled triangle be x m and the other side be (x + 4) m.

On applying Pythagoras theorem, we have: 

20² = (x + 4)² + x² 

⇒ 400 = x² + 8x + 16 + x² 

⇒ 2x² + 8x – 384 = 0 

⇒ x² + 4x – 192 = 0

⇒ x² + (16 – 12)x – 192 = 0 

⇒ x² + 16x – 12x – 192 = 0 

⇒ x²(x + 16) – 12(x + 16) = 0 

⇒ (x + 16) (x – 12) = 0 

⇒ x = –16 or x = 12 

The value of x cannot be negative.

Therefore, the base is 12 m and the other side is {(12 + 4) = 16 m}.