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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 тАУ 7
and hypotenuse = 13 cm
=> By Pythagoras Theorem
(Hypotenuse)2┬а= (Base)2┬а+ (Height)2
(13 )2┬а= x2┬а+(x тАУ 7)2
=> 169 = x2┬а+ x2┬атАУ 14x + 49
=> 2x2┬атАУ 14x + 49 тАУ 169 = 0
=> 2x2┬атАУ 14x тАУ 120 = 0
=> x2┬атАУ 7x тАУ 60 = 0 (Dividing by2)
Hence required quadratic equation will be x2┬атАУ7x тАУ 60 = 0

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