Question

Find the side and perimeter of a square whose diagonal is 10√2 cm​

Answer 1

Answer:

$\bigstar{\bold{Side\:of\:the\:square=10\:cm}}$

$\bigstar{\bold{Perimeter\:of\:the\:square=40\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\rm{Given:}}}}$

• Diagonal of the square =  10√2 cm

$\Large{\underline{\underline{\rm{To\:Find:}}}}$

• Side of the square
• Perimeter of the square

$\Large{\underline{\underline{\rm{Solution:}}}}$

➔ Here we are given the diagonal of the square.

➔ We know that,

    Diagonal of a square = √2 × a

    where a is a side of the square

➔ Substituting the given data, we get the value of a

    10√2 = √2 a

➔ Cancelling √2 on both sides,

    10 = a

    a = 10 cm

➔ Hence the side of the square is 10 cm

    $\boxed{\bold{Side\:of\:the\:square=10\:cm}}$

➔ Now we have to find the perimeter of the square.

➔ The perimeter of a square is given by,

    Perimeter of a square = 4 × side

➔ Substitute the value for side,

    Perimeter of the square =  4 × 10

    Perimeter of the square = 40 cm

➔ Hence the perimeter of the square is 40 cm

    $\boxed{\bold{Perimeter\:of\:the\:square=40\:cm}}$

$\Large{\underline{\underline{\rm{Notes:}}}}$

➔ The diagonal of a square is given by,

    Diagonal of a square = √2 a

➔ The perimeter of a square is given by

    Perimeter of a square = 4a

➔ The area of a square is given by,

    Area of a square = a²

   Where a is a side of the square.