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Q.4 Which of the following can be the sides of a right triangle?
(i) 2.5 cm, 6.5 cm, 6 cm.
(ii) 2 cm, 2 cm, 5 cm.
(iii) 1.5 cm, 2 cm, 2.5 cm
Answer :

(i) Given sides are 2.5 cm, 6.5 cm, 6 cm.
Square of the longer side = \((6.5)^2 = 42.25 \) cm.
Sum of the square of other two sides = \( (2.5)^2 + (6)^2 = 6.25 + 36 \) = 42.25 cm.
Since, the square of the longer side in a triangle is equal to the sum of the squares of other two sides.
\(\therefore \)The given sides form a right triangle.

(ii) Given sides are 2 cm, 2 cm, 5 cm .
Square of the longer side =\( (5)^2 = 25 \)cm
Sum of the square of other two sides =\( (2)^2 + (2)^2 =4 + 4 = 8 cm \) Since 25 cm \(\neq \)8 cm
\(\therefore \)The given sides do not form a right triangle.

(iii) Given sides are 1.5 cm, 2 cm, 2.5 cm
Square of the longer side = \( (2.5)^2 = 6.25 \)cm
Sum of the square of other two sides = \((1.5)^2 + (2)^2 = 2.25 + 4 = 6.25cm = 6.25 cm = 6.25 cm \)
Since the square of longer side in a triangle is equal to the sum of square of other two sides.
\(\therefore \)The given sides form a right triangle.