In a rectangle, one side is 24cm and the diagonal is 25cm. Find the perimeter of the rectangle.

In a rectangle, the diagonal forms a right-angled triangle with sides, where the diagonal is the hypotenuse.

Hypotenuse length formula:

a ^ 2 = b ^ 2 + c ^ 2, where a is the hypotenuse, b and c are legs.

Let us express one of the legs from the formula:

c ^ 2 = a ^ 2 – b ^ 2.

c = √ (a ^ 2 – b ^ 2).

Find the second side of the rectangle:

c = √ (25 ^ 2 – 24 ^ 2) = √ (625 – 576) = √49 = 7 cm – the length of the second side.

Formula for the perimeter of a rectangle:

P = (a + b) * 2, where a and b are the sides of the rectangle.

P = (24 + 7) * 2 = 31 * 2 = 62 cm – the perimeter of the rectangle.

Answer: P = 62 cm.