the length of the side of right angled triangle are ( 2x+ 1),cm, 2x cm,( x- 1 )cm .find x.
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Longest side = Hypotenuse = 2x + 1
By Pythagoras theoram,
(2x +1)^2 = (2x)^2 + (x-1) ^2
=> 4x^2 + 1 + 4x = 4x^2 + x^2 + 1 - 2x
=> 4x = x^2 - 2x
=> x^2 - 2x - 4x = 0
=> x^2 - 6x = 0
=> x (x - 6) = 0
=> x - 6 = 0
=> x = 6
Hypotenuse = 2 × 6 + 1 = 12 + 1 = 13 cm
Base = 2 × 6 = 12 cm
Perpendicular = 6 - 1 = 5 cm
By Pythagoras theoram,
(2x +1)^2 = (2x)^2 + (x-1) ^2
=> 4x^2 + 1 + 4x = 4x^2 + x^2 + 1 - 2x
=> 4x = x^2 - 2x
=> x^2 - 2x - 4x = 0
=> x^2 - 6x = 0
=> x (x - 6) = 0
=> x - 6 = 0
=> x = 6
Hypotenuse = 2 × 6 + 1 = 12 + 1 = 13 cm
Base = 2 × 6 = 12 cm
Perpendicular = 6 - 1 = 5 cm
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