A rectangle has two sides of length 3 cm and diagonals of length 5 cm. Calculate the length of the other two sides.

The rectangle in question is actually a right-angled triangle, with the two sides of length 3 cm forming the base and height, and the diagonal of length 5 cm forming the hypotenuse.

We can use the Pythagorean theorem to find the length of the other two sides. The 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 lengths of the other two sides.

In mathematical terms, this can be written as: a² + b² = c²

In this case, we know that a = b = 3 cm (the lengths of the two sides) and c = 5 cm (the length of the diagonal).

Substituting these values into the equation gives us:

3² + 3² = 5² 9 + 9 = 25 18 = 25

This equation is already satisfied, which means that the lengths of the other two sides of the rectangle are also 3 cm.

So, the rectangle is actually a square with all sides of length 3 cm.