Question

if diagonal of a square is √2cm then the perimeter of a square is.... cm​

Answer 1

Answer:

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Answer 2

Concept

A square is a quadrilateral with all four sides equal and perpendicular to one another.

Given

The length of the diagonal of the square is $\sqrt{2}cm$.

To Find

The perimeter of the square.

Solution

By Pythagoras theorem,

$(hypotenuse)^2=(base)^2+(height)^2$

According to the question, hypotenuse is the diagonal, and base and height are the length of the sides of the square which are equals. So, we can write-

$(\sqrt2)^2=(side)^2+(side)^2\\2(side)^2=2\\side=1cm$

The perimeter of the square is 4 times the length of the side of the square.

So, perimeter is-

$P=4\times 1\\p=4cm$

Hence, the perimeter of the square is 4cm whose length of the diagonal is $\sqrt2 cm$.

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