Question

Choose the correct statements.
(i) 8, 15, 17 is a Pythagorean triplet.
(ii) The hypotenuse of a right-angled triangle whose sides are 9 cm and 40 cm is 41 cm.
(iii) Pythagoras theorem is true for all types of triangles.
(iv) The hypotenuse of a right-angled triangle whose sides are 7 cm and 24 cm is 26 cm.
(2 marks)

Answer 1

(i) Since $8^2+{15}^2={17}^2,$ the numbers 8, 15 and 17 form a Pythagorean triplet.
(0.5 marks)
(ii) In a right-angled triangle, the square of the hypotenuse is equal to th sum of the squares of the other two sides.
Thus, if the sides are 9 cm and 40 cm, then the hypotenuse is given by $\sqrt{9^2+{40}^2}$ cm = 41 cm.
(0.5 marks)
(iii) Pythagoras' theorem holds good for right-angled triangles. Though any triangle can be split into 2 right-triangles and Pythagoras' theorem can be applied to the right-triangles, we cannot apply the theorem directly to any given triangle in general.
(0.5 marks)
(iv) Using Pythagoras' theorem, we get the hypotenuse equal to $\sqrt{7^2+{24}^2}=\sqrt{625}=25\text{cm}.$
Thus, the statement is false.
(0.5 marks)