Final answer:
The side length of a square is given as (2x + 3), and by squaring this value, we obtain the area of the square. The Pythagorean theorem is used to calculate the diagonal of the square as (2x + 3)√2.
Step-by-step explanation:
Given that the figure is a square and the area is represented by an expression, we can denote the side length of the square as (2x + 3). To prove this, we will use geometric properties and the definition of area for a square, which is side length squared, or a². Since a square has all sides equal, if the area is expressed as the square of (2x + 3), then this must indeed be the length of one side.
To calculate the area of the square, we simply square the side length, which gives us (2x + 3)². If we want to determine the measurement of the diagonal of the square, we can apply the Pythagorean theorem. According to the theorem, the diagonal of a square, which is also the hypotenuse of a right-angled triangle with sides equal to the square, is given by the formula: c = √(a² + b²). Since a = b in a square, the formula for the diagonal becomes c = √(2 * (2x + 3)²), which simplifies to c = (2x + 3)√2, revealing the relationship between the side length and the diagonal.