Question
The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
Hint:
Sides containing right angle are height and base.
The correct answer is: 60 cm
It is given that difference between perpendicular and base = 14 cm
i.e. b – h = 14 ⇒ b = 14 + h
Now, Area of triangle = 120 cm2
= 120
= 240
h2 + 14h – 240 = 0
h = 
h = 
h = 10 , - 24
Since, perpendicular is always positive so h = 10
Base, B = 14 + 10 = 24
Using Pythagoras theorem ,
H2 = B2 + P2
H2 = 242 + 102 = 576 + 100 = 676
H = 
= 26 cm
Perimeter of triangle = Sum of all sides
= 24 + 10 + 26 = 60 cm
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