Q. 694.8( 4 Votes )

The hypotenuse of a right – angled triangle is 20 meters. If the difference between the lengths of the other side’s be 4 meters, find the other sides.

Answer :

Let one side of right – angled triangle be x m and other side be x + 4 m

On applying the Pythagoras theorem –


202 = (x + 4)2 + x2


400 = x2 + 8x + 16 + x2


400 = 2x2 + 8x + 16


2x2 + 8x – 384 = 0


x2 + 4x – 192 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 4 c = – 192


= 1. – 192 = – 192


And either of their sum or difference = b


= 4


Thus the two terms are 16 and – 12


Difference = 16 – 12 = 4


Product = 16. – 12 = – 192


x2 + 16x – 12x – 192 = 0


x(x + 16) – 12(x + 16) = 0


(x + 16) (x – 12) = 0


x = 16 or x = 12


x cannot be negative


Base is 12m and other side is 12 + 4 = 16m


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
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Balance the Chemical Equations49 mins
Champ Quiz | Quadratic Equation48 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