Question

If the length of the diagonal of a square is 5√ 2cm then the length of its each side is​

Answer 1

$\sf\huge\bold{Solution}$

Given

Length of diagonal of square is 5√2 cm

To Find

Length of each side

We know that :

D=√2a ,where a is side

$= > a = \sqrt{2} \dfrac{d}{2}$

$= > a = \sqrt{2} \times \dfrac{5 \sqrt{2} }{2}$

2 can also be written as √2×√2

$= > a = \dfrac{{\cancel{ \sqrt{2}}} \times 5 \sqrt{2} }{ {\cancel{\sqrt{2}}} \times \sqrt{2} }$

$= > a = \dfrac{ 5{\cancel{\sqrt{2}}} }{{\cancel{ \sqrt{2} }}} = 5$

$\sf \therefore \:length \: of \: each \: side \: is \: 5cm$

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Extra solved=>

Perimeter of square is 4a

=>4×5=20cm

Area of square is (side)²

=>(5)²=25cm²

Answer 2

Answer:

• length of its sides is 5cm
• Area of square is 25cm²

Given:

• The length of the Diagonal a square is 5√ 2cm

To find:

• length of its sides and area of square

Solution:

Method (2) :

• Let its sides be x

• Length of Diagonal is 5√ 2cm

As we know that:

• Pythagoras theorem = h² = p² + b²

so,

$\sf{ : \implies \: (5 \sqrt{2}) {}^{2} = {x}^{2} + {x}^{2})}$

$\sf{ : \implies \: 25 \times 2 = 2 {x}^{2}}$

$\sf{ : \implies \: {x}^{2} = 25}$

$\sf{ : \implies \:x = \sqrt{25}}$

$\sf{ : \implies \: x= 5}$

$\sf \underline{ \therefore \: length \: of \: its \: sides \: is \: 5cm}$

✪ Now we have to find Area of square

As we know that:

• Area of square = side × side

$\sf{ : \implies 5\times 5}$

$\sf{ : \implies \: 25{cm}^{2} }$

Method (2) :

• Given Diagonal is 5√ 2cm then,

$\sf{ : \implies 5 \sqrt{2}cm = ( \sqrt{2)} \times side}$

$\sf{ : \implies side \: = \dfrac{5 \sqrt{2}cm }{( \sqrt{2)} }}$

$\sf{ : \implies side = 5cm}$

• Now area of square = side × side

$\sf{ : \implies 5\times 5}$

$\sf{ : \implies \: 25{cm}^{2} }$

$\sf \underline{ \therefore \: length \: of \: its \: sides \: is \: 5cm}$

$\sf \underline{ \therefore \:Area \: of \: square \: is \: 25 {cm}^{2} }$