Question

if the length of a diagonal of square is 20 CM. find

a ) side of square
b ) perimeter of the square ​

Answer 1

Answer :-

a.) Side of the square = (20 cm × √2)/2

b.) Area of the square = 400 cm²

Given :-

Diagonal of square = 20 cm

To find :-

a ) side of square

b ) perimeter of the square

Solution :-

We have diagonal of the square. We will use diagonal of a square formula to find the side of the square. Then, we will find area of square by the side of the square.

First, finding side,

Diagonal of a square = side × √2

=> 20 cm = s × √2

$= > \tt{\dfrac{20 \: cm}{ \sqrt{2} } = s} \\ \\ \tt{multiplying \: \: \sqrt{2} \: \:to\: \: the \: \: fraction } \\ \\ = > \tt{\dfrac{20 \: cm \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } = s} \\ \\ = > \tt{\dfrac{20 \: cm \times \sqrt{2} }{ 2 } = s}$

Now, we have side of the square. We will find area with the help of the side of the square.

Area of square = (side)²

$\tt{=> A =(\dfrac{20 \: cm \times \sqrt{2} }{ 2})^{2} } \\ \\ \tt{=> A =\dfrac{20 \: cm \times \sqrt{2} }{ 2} \times \dfrac{20 \: cm \times \sqrt{2} }{ 2}} \\ \\ \tt{=> A =\dfrac{800 \: cm^{2} }{ 2}}\\ \\ \tt{=> A = 400 \: cm^{2} }$

More Information :-

• Area of square = (Side)²

• Area of rectangle = Length × Breadth

• Perimeter of square = 4 × side

• Perimeter of rectangle = 2(Length + Breadth)

• Area of rhombus = 1/2 × First Diagonal × Second Diagonal