Question

Find the side and pesimeter of a squase whose diagonal is 10 cm
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Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given that diagonal of a square is 10 cm

To Find:

• We have to find the value of side and perimeter of given square

Concept Used:

Side of the square can be determined by using the following formula :

$\boxed{\sf{Diagonal = Side \: \sqrt{2 \: }}}$

After determining the side of square its perimeter can easily be determined by using :

$\boxed{\sf{Perimeter \: of \: Square = 4 \times Side }}$

$\sf{ }$

Solution:

We have been given that

$\boxed{\sf{Diagonal \: of \: Square = 10 \: cm}}$

Let the side of square = x

$\odot \:$ Side of Square :

Using formula of diagonal of square which is the product of side to the square root of 2

$\implies \sf{Diagonal = 10 \: cm}$

$\implies \sf{Side \: \sqrt{2 \: }= 10 }$

Substituting the values in Equation

$\implies \sf{x \: \sqrt{2 \: }= 10 }$

$\implies \sf{x= \dfrac{10}{\sqrt{2 \: }} }$

$\implies \sf{x= \dfrac{10}{\sqrt{2 \: }} \times \dfrac{\sqrt{2 \: }}{\sqrt{2 \: }}}$

$\implies \sf{x= \dfrac{10 \: \sqrt{2 \: }}{2} }$

$\implies \boxed{\sf{x = 5 \: \sqrt{2 \: }}}$

$\sf{ }$

$\odot \:$Perimeter of Square :

Using formula of perimeter of square

$\implies \sf{Perimeter = 4 \times side }$

$\implies \sf{Perimeter = 4 \times x }$

$\implies \sf{Perimeter = 4 \times 5 \: \sqrt{2 \: }}$

$\implies \boxed{\sf{Perimeter = 20 \: \sqrt{2 \:}}}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Diagonal = 5 \: \sqrt{2 \: } \: cm}}$

$\large\boxed{\sf{Perimeter = 20 \: \sqrt{2 \: } \: cm}}$

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$\large\purple{\underline{\underline{\sf{Extra \: Information:}}}}$

• A square is a polygon with 4 sides of equal length and 4 right angle corners
• The perimeter of a square is 4 times the length of one side.
• Length of both diagonal of a square are equal
• The diagonals of a square bisect each other at 90 degrees and are perpendicular.
• Opposite sides of a square are parallel.
• The internal angles of a square add to 360 degrees.