Answer :

(i) True


Let the sides of triangle be 3x, 4x and 5x.


By applying Pythagoras theorem to this triangle, we get,


(5x) 2 = (3x) 2 + (4x) 2


25x2 = 9x2 + 16x2


25x2 = (9 + 16)x2


25x2 = 25x2


Thus, all triangles having sides in ratio 3:4:5 will form right angled triangle.


(ii) False


Given: Length of chord = 10 cm


Since, the chord subtends right angle at the centre, then the triangle is a right angled triangle.


Let the radius of circle be x.


By applying Pythagoras theorem to this triangle we get,


102 = x2 + x2


100 = 2x2


2x2 = 100


x2 = 50


x = √50 = 2√5 cm


It is found that the radius of the circle must be 2√5 cm which mismatch from the radius given in question as 5 cm. Hence, it is false statement.


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