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+x^2` 

⇒`4x^2-4x+1=x^2+2x+1+x^2` 

⇒ `2x^2-6x=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 =`(2xx3-1)=5m` 

Third side = `(3+1)=4m`