Problem: Find the area of a square whose length of the diagonal is 2.4 m.

Solution:

To find the area of the square, we need to determine the length of its sides first. Since the diagonal of the square is given, we can use the Pythagorean theorem to find the length of its sides.

Using the Pythagorean theorem:

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the square acts as the hypotenuse, and the sides of the square act as the other two sides of the right-angled triangle.

Let's assume the length of one side of the square as 's'.

So, according to the Pythagorean theorem:

s² + s² = (2.4)²

Simplifying the equation:

2s² = 2.4²

2s² = 5.76

Finding the length of one side:

Dividing both sides of the equation by 2:

s² = 2.88

Taking the square root of both sides:

s ≈ √2.88

s ≈ 1.697 m

Finding the area of the square:

The area of a square is given by the formula:

Area = side²

Substituting the value of 's':

Area ≈ (1.697)²

Area ≈ 2.88 m²

Answer: The area of the square is approximately 2.88 square meters.

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