Q4 of 168 Page 7

Represent the following situations in the form of the quadratic equation.

The hypotenuse of a right-angled triangle is 6 metres more than twice of the shortest side. The third side is two metres less than the hypotenuse.

Let ‘x’ be the length of the shortest side.

∵ The hypotenuse of a right−angled triangle is 6 metres more than twice of the shortest side.


∴ length of hypotenuse = 2x + 6


∵ The third side is two metres less than the hypotenuse.


∴ length of third side = hypotenuse – 4 = 2x + 4


By applying Pythagoras theorem; Hypotenuse square is equal to sum of the squares of other two sides.


⇒ (2x + 6)2 = x2 + (2x + 4)2


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