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.


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.


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.


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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