Question

6.
Find the side and perimeter of a square whose diagonal is 10 cm.
​

Answer 1

Answer:

Diagonal of a square=

2

a

where

a=side

10=

2

a

a=

2

10

a=5

2

cm

Perimeter of square=4a

=4×5

2

=20

2

Therefore side and perimeter of the square is 5

2

cm and 20

2

cm

Answer 2

Diagonal = 10cm

The diagonals of a square are equal.

Also, A square is also a rhombus.

Area of rhombus = $\rm \frac{d_1 d_2}{2}$

=> 10 X 10/ 2

=> 100/2

=>$\rm 50 cm^2$

Area of square = $a^2$

$\therefore \rm a^2 = 50cm^2 \\ \implies \rm a = \sqrt{50cm^2} \\ \implies \rm a = 7.07 \: \: (approx.)$

Hence, side of the square is 7.07cm

Perimeter of square = 4a

=> $4 \times 7.07$

=> 28.2 cm

Hence, the perimeter of the square is 28.2 cm