Question

If the length of the diagonal of a square is 20cm,then it's perimeter is
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Answer 1

Answer:

40√2 cm

Step-by-step explanation:

Heya !!!

This is your answer.

Given :-

Diagonal of square = 20 cm.

We know that Area of Square =

1/2 × d²

= 1/2 × 20 × 20

= 10×20

= 200 cm².

Also, area = side²

So,

side = √area

side = √200

Side = 10√2 cm.

Perimeter= 4 × side

= 4 × 10√2

= 40√2 cm.

Hence the perimeter of the square is 40√2 cm.

Hope it helps

Answer 2

In square ABCD, diagonal AC makes two triangles ADC and ABC.

Interior angles of square are equal and 90°

Hence, the triangles formed are right angled triangle.

In △ABC, AC is given which hypotenuse, so by using pythagoras theorem of right angled triangle we can find the sides of the square

${AC}^{2} = {AB}^{2} + {BC}^{2} \\ {20}^{2} = {a}^{2} + {a}^{2} \\ 2 {a}^{2} = 400 \\ {a}^{2} = 200 \\ a = \sqrt{200} = 2 \sqrt{50}$

Now, we have the sides of the square, we can find the perimeter of square.

Perimeter of square, P = 4 times sides of square

$P = 4 \times 2 \sqrt{50} = 8 \sqrt{50} = 8 \times 7.071 = 56.568 \: cm$