Question

The diagonal of a square is 10√2 units.
Find lengths of its sides and its perimeter.​

Answer 1

Answer :

• s = 10 cm
• P = 40 cm

Given :

• The figure is square
• Diagonal

To find :

• The length of the side
• Perimeter

Solution :

Let each side of the square be s units.

Using PGT in right angled ∆ABC :

AC² = AB² + BC²

$\implies$ (10√2)² = s² + s²

⇢200 = 2s²

⇢200/2 = s²

⇢s² = 100

⇢s = √100

⇢s = 10 units

$\boxed{ \therefore \sf the \: side \: of \: the \: square \: is \: 10 \: units .}$

Perimeter of a square = 4 × side

= 4 ×10

= 40 units

$\boxed{ \therefore \sf the \: perimeter \: of \: the \: square \: is \: 40 \: units.}$

Refer to the attached figure .

______________________

A square is a parallelogram with all sides equal and measure of all angle 90° .

The diagonal of any square with edge e is given by e√2 .

Answer 2

Given ,

• The diagonal of a square is 10√2 units

We know that , the diagonal of square is given by

Diagonal = a√2 , a = side

Thus ,

10√2 = a√2

a = 10 units

$\sf \therefore \underline{The \: side \: of \: square \: is \: 10 \: units }$

Now , the perimeter of square is given by

Perimeter = 4a

Thus ,

Perimeter = 4 × 10

Perimeter = 40 units

$\sf \therefore \underline{The \: perimeter \: of \: square \: is \: 40 \: units }$