Question

The diagonal of a square is 8 cm.

What is the length of the side of this square?
Give your answer as an exact surd in its simplest form

Answer 1

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 = √(2) (d)/(2)}}`

Where :

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

Solution :

Substituting the given value in the required formula :

`{\dashrightarrow{\pmb{\sf{ \: a = √(2) (d)/(2)}}}}`

`{\dashrightarrow{\sf{ \: a = √(2) * (8)/(2)}}}`

`{\dashrightarrow{\sf{ \: a = √(2) * \cancel{(8)/(2)}}}}`

`{\dashrightarrow{\sf{ \: a = √(2) * 4}}}`

`{\dashrightarrow{\sf{ \: a = 4√(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}}`

Answer 2

the length of the side of this square is
`4√(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=
`(64)/(2)`

a²=32

doing square root on both side

`√(a²)=√(32)`

a=±
`√(2*2*2*2*2)`

a=±2*2
`√(2)`

Since side of square is always positive so

a=4
`√(2)` or 5.65 cm