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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

(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.