Question

The perimeter of a square is 40 cm. Find the length of its diagonal​

Answer 1

Answer:

Perimeter of square = 4 × side

4 × side = 40

side = 40/4 = 10 cm

Diagonal of square = $\sqrt{2} \times side$

                                 = $\sqrt{2} \times 10$

                                 = $10\sqrt{2} \: cm$

                               

Answer 2

✧ Given :

• Perimeter of a square = 40 cm

✧ To find :

• Length of its diagonal.

✧ Solution :

Perimeter = 40 cm

4 × length = 40 cm

→ Length = 40 / 4 = 10 cm

→ Length = 10 cm

Area of square = Length × Length sq. units

Area = 10 × 10 sq. cm

→ Area = 100 sq. cm

So in a square , all sides are equal , Hence the diagonal will be calculated using the pythagoras theorem.

Let the Square be ABCD , So let the diagonal be AC ( Refer the attachment )

By Pythagoras theorem ,

${(AC)}^{2} = {(AB)}^{2} + {(BC)}^{2}$

${(AC)}^{2} = {(10)}^{2} + {(10)}^{2}$

${(AC)}^{2} = 200$

$AC = \sqrt{200}$

$\therefore \: AC = 14.1cm$

The length of the diagonal will be 14.1 cm

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