Q22 of 83 Page 90

The sides of a right angled triangle are x, x + 3, x + 6, x being a positive integer. Find the perimeter of the triangle.



According to Pythagoras theorem,


Hypotenuse2 = Base2 + Perpendicular2


⇒ (x + 6)2 = x2 + (x + 3)2


⇒ x2 + 36 + 12x = x2 + x2 + 9 + 6x


⇒ x2 – 6x – 27 = 0


⇒ x2 – (9 – 3)x – 27 = 0


⇒ x2 – 9x + 3x – 27 = 0


⇒ x(x – 9) + 3(x – 9) = 0


⇒ (x – 9)(x + 3) = 0


⇒ x = 9 or x = – 3


But side can’t be negative.


⇒ x(Base) = 9 cm.


⇒ Perpendicular = x + 3


= 12 cm


And, hypotenuse = x + 6


= 15 cm


∴ the Perimeter = sum of all 3 sides


= 9 + 12 + 15


= 36 cm


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