Q. 135.0( 2 Votes )

Hypotenuse of a right angled triangle is 2 less than 3 times its shortest side. If the remaining side is 2 more than twice the shortest side, find the area of the triangle.

Answer :

Let length of shortest side(base) be x.

hypotenuse = 3x – 2.


remaining side(perpendicular) = 2x + 2



Now, According to Pythagoras theorem,


Hypotenuse2 = Base2 + Perpendicular2


(3x – 2)2 = x2 + (2x + 2)2


9x2 + 4 – 12x = x2 + 4x2 + 4 + 8x


4x2 – 20x = 0


Dividing the whole equation by 4, we get –


x2 – 5x = 0


x(x – 5) = 0


x = 0 or x – 5 = 0


But side cannot be zero


x(Base) = 5


Perpendicular = 2x + 2


= 2(5) + 2


= 12


hypotenuse = 3x – 2


= 3(5) – 2


= 13


Now, area of right triangle –




= 30 sq. unit.


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
RELATED QUESTIONS :