Question

12.In a square of side 10 cm, its diagonal = ... (a) 15 cm (b) 10V2 cm (c) 20 cm (d) 12 cm
1)
2)
3)
4)​

Answer 1

Step-by-step explanation:

ABCD is an Square having length of sides a and d is its diagonal.

Here sides AB = BC = CD = DA = a = 10 cm

Now consider the triangle ABC,which is a right angle triangle with ∠B = 90°

By Pythagoras theorem:

AC² = AB² + BC²

d² = a² + a²

d² = (10cm)² + (10cm)²

d² = 200 cm²

So, d = √ (200cm²) = (10√ 2)cm

Now because every squares have two diagonals of equal length, So Diagonal AC = BD = d = (10√ 2)cm

Answer 2

Diagonal of a circle with side $10 cm$ is (b)$10\sqrt{2} cm$.

Step-by-step explanation:

Given:

Square with side = $10 cm$

To find: Diagonal of square

Calculation:

Side of square $=10 cm$

Each angle in square is $90^{o}$. When a diagonal is drawn, the square is parted in two right-angled triangle.

Diagonal becomes the hypotenuse and two sides of square becomes a base and a perpendicular of the triangle. Let the hypotenuse or the diagonal of square be $h$.

So, by Pythagoras theorem: Square of hypotenuse is equal to the sum of squares of base and perpendicular of right angled triangle.

$AC =\sqrt{AB^{2}+BC^{2} }\\h=\sqrt{10^{2}+10^{2} } \\h=\sqrt{200}=10\sqrt{2}$

Therefore, diagonal of square = $h=AC=10\sqrt{2} cm$.