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The hypotenuse of a right – angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.


Let the shortest side of triangle be xm

According to the question ;


Hypotenuse = 2x – 1 m


Third side = x + 1 m


Applying Pythagoras theorem


(2x – 1)2 = (x + 1)2 + x2


4x2 – 4x + 1 = x2 + 2x + 1 + x2 using (a – b)2 = a2 – 2ab + b2


2 x2 – 6x = 0


2x (x – 3) = 0


x = 0 or x = 3


Length of side cannot be 0 thus the shortest side is 3m


Hypotenuse = 2x – 1 = 6 – 1 = 5m


Third side = x + 1 = 3 + 1 = 4m


Thus the dimensions of triangle are 3m, 4m and 5m.


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