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

4
`√(2)` cm

Explanation:

The diagonal divides the square into 2 right angles with legs s and the diagonal as the hypotenuse.

Using Pythagoras' identity in the right triangle , then

s² + s² = 8²

2s² = 64 ( divide both sides by 2 )

s² = 32 ( take the square root of both sides )

s =
`√(32)` = 4
`√(2)`

Answer 2

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}}`