Answer :

(i) In a right angled triangle, the area of square drawn on the hypotenuse is equal to the SUM of the areas of the squares drawn on the other two sides.


Explanation:


It is inferred from expression of Pythagoras theorem i.e.


H2 = P2 + B2


(ii) In an isosceles right-angled triangle if the length of each of two equal sides is 42 cm, then the length of the hypotenuse will be 42√2 cm.


Explanation:


By Pythagoras theorem we get,


h2 = 422 + 422


h2 = 1764 + 1764


h2 = 3528


h = √3528 = 42√2 cm


(iii) In a rectangular figure ABCD, the two diagonals AC and BD intersect each other at point O, if AB = 12 cm, AO = 6.5 cm, then the length of BC is 5 cm.


Explanation:



We know that, diagonals of a rectangle bisect each other.


So, AC = 2 × AO


AC = 2 × 6.5


AC = 13 cm


Now, applying Pythagoras theorem to ΔABC gives,


132 = 122 + BC2


169 = 144 + BC2


BC2 = 169-144 = 25


BC = √25 = 5 cm


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