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General

Easy

Question

# The lengths of the two sides of right triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm^{2}. Find the perimeter of triangle

Hint:

### Sides containing right angle are height and base.

## The correct answer is: 24 cm

### It is given that difference between perpendicular and base = 2 cm

i.e. b – h = 2 ⇒ b = 2 + h

Now, Area of triangle = 24 cm^{2}

= 24

= 48

h^{2} + 2h – 48 = 0

h =

h =

h = 6 , - 8

Since, perpendicular is always positive so h = 6

Base, B = 2 + 6 = 8

Using Pythagoras theorem ,

H^{2} = B^{2} + P^{2}

H^{2} = 8^{2} + 6^{2} = 64 + 36 = 100

H = = 10 cm

Perimeter of triangle = Sum of all sides

= 8 + 10 + 6 = 24 cm

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