Q. 244.4( 10 Votes )

The hypotenuse of a right–angled triangle is 6 cm more than twice the shortest side. If the third side is 2 cm less than the hypotenuse, find the sides of the triangle.

Answer :

Let the shortest side(AC) be ‘(X)’cms, so the hypotenuse (BC) will be ‘(2X+6)’ cms, as demonstrated in the figure drawn below:

AB = 2X + 4 cms

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

(2X + 6)2 = X2 +(2X + 4)2

On simplifying further,

4X2 + 24X + 36 = X2 + 4X2 + 16X + 16

Using the identity of a2 + b2 + 2ab = (a + b)2

X2 – 8X – 20 = 0 –––––– (i)

On applying Sreedhracharya formula

X = –2 or 10.

the shortest side (AC) is X = 10 cms (Only positive values), hypotenuse (2X+6) i.e., (BC) is 26 cms and the other side (AB) is (2X+4) i.e., 24 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 Equations51 mins
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
Understand The Concept of Quadratic Equation45 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