Q15 of 27 Page 289

Let us write whether the following statements are true or false:

(i) If the ratio of the lengths of three sides of a triangle is 3:4:5, then the triangle will always be a right angled triangle.


(ii) If in a circle of radius 10cm. length, a chord subtends right angle at the centre, then the length of the chord will be 5cm.

(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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