Question

Square abcd is made up of one inside square

Answer 1

Square ABCD is made up of one inside square.

Step-by-step explanation:

Square ABCD is composed of an inside square, and this arrangement can be visualized through a geometric analysis. Consider a square with side length
`\( s \)` representing the outer square, and within it, there exists a smaller square.

Let
`\( s_i \)` denote the side length of the inside square. To determine the relationship between the side lengths, we can observe that the corners of the inside square touch the midpoints of the sides of the outer square. This creates four right-angled triangles, each with legs
`\( (s)/(2) \)` and
`\( (s_i)/(2) \).` Applying the Pythagorean theorem, we have
`\( ((s)/(2))^2 + ((s_i)/(2))^2 = s^2 \),` which simplifies to
`\( s_i = (s)/(√(2)) \).`

Therefore, the side length of the inside square
`(\( s_i \))` is equal to
`\( (s)/(√(2)) \),`confirming that Square ABCD is indeed made up of one inside square. This relationship between the side lengths ensures that the corners of the inside square align with the midpoints of the outer square's sides, creating a geometrically cohesive structure. This analysis highlights the inherent symmetry and mathematical precision involved in the configuration of Square ABCD.