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ak78
Assume s is the side of the first square.
Let's find out the value of s:
4^2 = 2 × s^2 => s = 2.83 meters

Assume S is the side of the second square. Therefore 2.83^2 = 2 × S^2 => S = 2 meters.

The side of the second square is 2 meters

The side of the second square is: 2 meters.

To find the side of the second square, we have to:

  • First, find the side of the first square, applying the Pythagorean Theorem.
  • Apply the Pythagorean Theorem on the second square, considering that the diagonal is the side of the first square.

Pythagorean Theorem:

In a right triangle, the sum of the length of the sides squared is equals to the length of the hypotenuse squared, that is, considering sides a and b and hypotenuse c:

[tex]a^2 + b^2 = c^2[/tex]

The picture at the end of this exercise exemplifies the Theorem.

First square:

In a square, the sides have the same length, so:

  • The diagonal, of 4 meters, is the hypotenuse.
  • The sides are a, so:

[tex]a^2 + a^2 = 4^2[/tex]

[tex]2a^2 = 16[/tex]

[tex]a^2 = \frac{16}{2}[/tex]

[tex]a^2 = 8[/tex]

[tex]a = \sqrt{8}[/tex]

[tex]a = \sqrt{4*2}[/tex]

[tex]a = \sqrt{4}\sqrt{2}[/tex]

[tex]a = 2\sqrt{2}[/tex]

Second square:

  • Diagonal of [tex]2\sqrt{2}[/tex]
  • Sides of a.

Then:

[tex]a^2 + a^2 = (2\sqrt{2})^2[/tex]

[tex]2a^2 = 8[/tex]

[tex]a^2 = \frac{8}{2}[/tex]

[tex]a^2 = 4[/tex]

[tex]a = \sqrt{4}[/tex]

[tex]a = 2[/tex]

Thus, the length of the side of the second square is of 2 meters.

A similar problem is given at https://brainly.com/question/21691542

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