Q. 664.7( 7 Votes )

The area of a right triangle is 600 cm2. If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.

Answer :

Let the altitude of the given triangle x cm

Thus the base of the triangle will be (x + 10)cm


Area of triangle =


x (x + 10) = 1200


x2 + 10x – 1200 = 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 = 10 c = – 1200


= 1. – 1200 = – 1200


And either of their sum or difference = b


= 10


Thus the two terms are 40 and – 30


Difference = 40 – 30 = 10


Product = 40. – 30 = – 1200


x2 + 40x – 30x – 1200 = 0


x(x + 40) – 30(x + 40) = 0


(x + 40)(x – 30) = 0


x = – 40, 30


x = 30 (altitude cannot be negative)


Thus the altitude of the given triangle is 30cm and base of the triangle = 30 + 10 = 40cm


Hypotenuse2 = altitude2 + base2


Hypotenuse2 = (30)2 + (40)2


= 900 + 1600 = 2500


Hypotenuse = 50 cm


Altitude = 30cm


Base = 40cm


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
Understand The Concept of Quadratic Equation45 mins
Balance the Chemical Equations49 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