Question

length of diagonal of a square is √128 .Find the length of the side and perimeter of the square​

Answer 1

Answer: 8, 32

Step-by-step explanation:

let side be x

Then, using Pythagorean theorem,

√(x square + x square ) = √128

Now, √ will get canceled and we will get,

2x square = 128

x square = 64

x = √64 = 8

Now, P = 8 * 4 = 32

Answer 2

Given :-

• Length of diagonal = $\sqrt{128}cm$

To Find :-

• Length of side
• Perimeter of the square

Solution :-

Length of Diagonal = $\sqrt{128}cm$

$\large{\boxed{\green{Diagonal\:of\:square\:=\: \sqrt{2}a}}}$

Where,

• a = Side of square

Substituting the value in the above formula,

$\sqrt{128}cm$ = $\sqrt{2}a$

$\sqrt{128}cm$ × $\sqrt{2}$ = a

$\sqrt{256}$ = a

$\huge{\boxed{\mapsto{\purple{a\:=\:16\:cm}}}}$

Perimeter :-

$\large{\boxed{\red{Perimeter\:of\:square\:=\:4 × Side}}}$

Substituting the value in the above formula,

$\implies{Perimeter\:=\:4 \times 16}$

$\huge{\boxed{\mapsto{\color{cyan}{Perimeter\:=\:64\:cm}}}}$

Hope it helps...........