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Question -

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.



Answer -

Let the base of a right triangle = x
Its height = x – 7
and hypotenuse = 13 cm
=> By Pythagoras Theorem
(Hypotenuse)2 = (Base)2 + (Height)2
(13 )2 = x2 +(x – 7)2
=> 169 = x2 + x2 – 14x + 49
=> 2x2 – 14x + 49 – 169 = 0
=> 2x2 – 14x – 120 = 0
=> x2 – 7x – 60 = 0 (Dividing by2)
Hence required quadratic equation will be x2 –7x – 60 = 0

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