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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Get To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Champ Quiz | Quadratic Equation33 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Balance the Chemical Equations49 mins
Know More About The Quadratic Formula43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses