Question

The hypotenuse of a right-angled triangle is 1 meter less than twice the shortest side. If the third side 1 meter more than the shortest side, find the side, find the sides of the triangle.

Answer 1

Let the shortest side be x m.

Therefore, according to the question: 

Hypotenuse = (2x – 1) m 

Third side = (x + 1) m

On applying Pythagoras theorem, we get: 

(2x – 1)² = (x + 1)² + x² 

⇒ 4x² – 4x + 1 = x² + 2x + 1 + x² 

⇒ 2x² – 6x = 0 

⇒ 2x(x – 3) = 0 

⇒ x = 0 or x = 3 

The length of the side cannot be 0; therefore, the shortest side is 3 m.

Therefore,  

Hypotenuse = (2 × 3 – 1) = 5 m 

Third side = (3 + 1) = 4 m