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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
Solution
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:
`20^2=(x+4)^2+x^2`
⇒` 400x^2+8x+16+x^2`
⇒ `2x^2+8x-384=0`
⇒`x^2+4x-192=0`
⇒`x^2+16x-12x-192=0`
⇒ `x^2(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)=16m}`
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