Let us fill in blanks:

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

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

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

(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