Question

The diagonal of a square is 8 cm.

Answer 1

the length of the side of this square is $4\sqrt{2} \:or \:5.65$cm

Answer:

Solutions Given:

let diagonal of square be AC: 8 cm

let each side be a.

As diagonal bisect square.

let it forms right angled triangle ABC .

Where diagonal AC is hypotenuse and a is their opposite side and base.

By using Pythagoras law

hypotenuse ²=opposite side²+base side²

8²=a²+a²

64=2a²

a²=$\frac{64}{2}$

a²=32

doing square root on both side

$\sqrt{a²}=\sqrt{32}$

a=±$\sqrt{2*2*2*2*2}$

a=±2*2$\sqrt{2}$

Since side of square is always positive so

a=4$\sqrt{2}$ or 5.65 cm

Answer 2

Answer:

Given :

↠ The diagonal of a square is 8 cm.

To Find :

↠ The length of the side of square.

Using Formula :

Here is the formula to find the side of square if diagonal is given :

$\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}}$

Where :

• ➺ a = side of square
• ➺ d = diagonal of square

Solution :

Substituting the given value in the required formula :

${\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}$

${\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}$

${\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}$

${\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}$

${\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}$

${\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}$

Hence, the length of the side of square is 5.6 cm.

$\underline{\rule{220pt}{3pt}}$