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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.
Solution
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`
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