Q. 26

The hypotenuse of a right triangle is 3√5cm. If the smaller side is tripled and the longer side doubled, new hypotenuse will be 9√5 cm. How long are the sides of the triangle?

Answer :

Let the shortest side(AC) be ‘(X)’cms, and the longer side (AB) be ‘(Y)’ cms, as demonstrated in the figure drawn below:



BC = 3√10 cms


(BC)2 = (AC)2 + (AB)2


(3√10)2 = X2 + (Y)2


On simplifying further,


(Y)2 = 90 – X2


X2 + Y2 – 90 = 0 –––––– (i)


As per the question,


New smaller side = ‘(3X)’ cms


New longer side = ‘(2Y)’ cms


BC = 9√5 cms


(BC)2 = (AC)2 + (AB)2


(9√5)2 = (3X)2 + (2Y)2


On simplifying further,


4Y2 + 9X2 = 405


4X2 + 9Y2 – 405 = 0 –––––– (ii)


Putting the value of X2, from equation (i) in equation (ii)


X2 = 90 – Y2


On simplifying further,


(360–4Y)2 + 9Y2 – 405 = 0


5Y2 = 45


Y = ± 3 cms(Only positive values),


X = √(90–9).


X = 9 cms


the shortest side (AC) is X = 9 cms hypotenuse i.e., (BC) is cms and the other side (AB) is 3 cms .


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