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General

Easy

Question

# The difference between the sides of the right angles triangle containing the right angle is 7 cm, and its area is 60 cm2 . Find the perimeter of the triangle.

Hint:

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

## The correct answer is: 40 cm

### It is given that difference between perpendicular and base = 7

i.e. b – h = 7 ⇒ b = 7 + h

Now, Area of triangle = 60 cm^{2}

= 60

= 120

h^{2} + 7h – 120 = 0

h^{2} +15h – 8h – 120 = 0

h(h + 15)-8(h + 15) = 0

(h + 15)(h – 8) = 0

h = 8 , - 15

Since, perpendicular is always positive so h = 8

Base, B = 7 + 8 = 15

Using Pythagoras theorem ,

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

H^{2} = 15^{2} + 8^{2} = 225 + 64 = 289

H = = 17 cm

Perimeter of triangle = Sum of all sides

= 17 + 8 + 15 = 40 cm

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