Respuesta :

evgeniylevi

Step-by-step explanation:

1) the length of the side is:

[tex]\frac{4-\sqrt{2} }{\sqrt{2}}=2\sqrt{2}-1.[/tex]

2) the required perimeter is:

[tex]P=4(2\sqrt{2} -1)=8\sqrt{2} -4.[/tex]

3) the required area is:

[tex]A=(2\sqrt{2} -1)^2=9-4\sqrt{2}.[/tex]

semsee45

Answer:

Side length = (2√2 - 1) units

Perimeter = (8√2 - 4) units

Area = (9 - 4√2) units²

Step-by-step explanation:

Properties of a square:

  • It is a quadrilateral
  • The opposite sides are parallel
  • All four sides are equal in length
  • All interior angles measure 90°

The diagonal of a square creates two right triangles, with the diagonal being the hypotenuse, and the sides of the square being the 2 legs.

Let x = side length of the square

Using Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ x² + x² = (4 - √2)²

⇒ 2x² = 18 - 8√2

⇒ x² = 9 - 4√2

⇒ x = ±(2√2 - 1)

⇒ x = 2√2 - 1  only (as distance is positive)

Perimeter of a square = 4x

                                    = 4(2√2 - 1)

                                    = 8√2 - 4

Area of a square = x²

                            = (2√2 - 1)²

                            = 9 - 4√2

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