Answer :


Let the base, perpendicular and Hypotenuse of right-angled triangle be b, p and h respectively.


We know, Perimeter of right-angled triangle = b + p + h


Given, perimeter = 30 cm


b + p + h = 30


b + p + 13 = 30 [ h, hypotenuse = 13 cm]


b = 17 – p [1]


Also, we know By Pythagoras theorem in right-angled triangle


(Hypotenuse)2 = (Base)2 + (Perpendicular)2


h2 = p2 + b2


(13)2 = p2 + (17 – p)2


169 = p2 + p2 + 289 – 34p


2p2 – 34p + 120 = 0


p2 – 17p + 60 = 0


p2 – 12p - 5p + 60 = 0


(p – 12)(p - 5) = 0


p = 12 cm or p = 5 cm


Case I: p = 12 cm


b = 17 – 12 = 5 cm


and we know, area of triangle



Case II: p = 5 cm


b = 17 – 5 = 12 cm


and we know, area of triangle



Therefore, Area of triangle is 30 cm2.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

The ratio of heigWest Bengal Mathematics

If length of eachWest Bengal Mathematics

The lengths of thWest Bengal Mathematics

If each side of aWest Bengal Mathematics

If the area, periWest Bengal Mathematics

D is such a pointWest Bengal Mathematics

The length of eacWest Bengal Mathematics

Look at the figurWest Bengal Mathematics

The length of hypWest Bengal Mathematics

An isosceles righWest Bengal Mathematics