Question

perimeter of square is 28root2 find diagonal​

Answer 1

Let the given square be ABCD.

Perimeter of square=28√2....... (Given)

since we know that,

Perimeter of a square=4×side

Let the side of the square be x.

28√2=4x

28√2/4=x

therefore, x=7√2

therefore, side of the square be 7√2

let AB=CD=7√2.....( All sides of square are congruent)

let AC be the diagonal of the square.

<A=<B=<C=<D=90°........ (Angles of a square)

therefore in triangle ABC, <ABC=90°

therefore, by Pythagoras thearom,

(AB) ²+(BC) ²=(AC) ²

(7√2) ²+(7√2) ²=(AC) ²

(AC) ²=98+98

(AC) ²=196

AC=14

therefore, diagonal of the square us 14

Answer 2

Answer:

The diagonal of square is 14 units.

Step-by-step-explanation:

NOTE: Kindly refer to the attachment first.

In fig., ⎕ ABCD is a square. [ Given ]

${P( \square\:ABCD ) = 28\sqrt{2}}$ [ Given ]

We know that,

${P({\square\:ABCD})=Perimeter \: of\:square}$

$\therefore\:{P({\square\:ABCD})=4\times\:side}$

$\therefore\:28\sqrt{2}=4\times\:side$

$\therefore\:Side=\frac{28\sqrt{2}}{4}$

$\boxed{Side\:of\:square\:=\:7\sqrt{2}\:units}$

$Now, \\\\We\:know\:that,\\\\Diagonal\:of\:square\:=side\sqrt{2}\\\\\therefore\:Diagonal\:of\:square=(7\sqrt{2})\times\sqrt{2}\\\\\therefore\:Diagonal\:of\:square=7\times\:2\\\\\therefore\boxed{Diagonal\:of\:square\:=\:14\:units}$

Additional Information:

1. Square:

A two dimensional figure having four equal sides and four angles of measurement 90° is called a square.

2. Perimeter:

The sum of lengths of the all sides of a particular figure is called perimeter.

3. Perimeter of square:

The perimeter of square means the sum of lengths of all sides of the square.

4. Formula for perimeter of square:

$\boxed{\sf\:Perimeter\:of\:square\:=\:4\times\:side}$

5. Diagonal of square:

The line segment joining the two opposite corners ( angles ) of the square is called a diagonal of square.

6. Formula for diagonal of square:

$\boxed{\sf\:Diagonal\:of\:square\:=\:side\:\sqrt{2}}$