Find the length of a rectangle if its width is 6 cm and the perimeter is 42.

Let’s denote: a – the length of the rectangle, b – its width, P – the perimeter of the rectangle.

It is known that the perimeter of a rectangle is equal to the sum of the lengths of all its sides:

P = a + b + a + b = 2a + 2b.

If we know the perimeter of the rectangle and its width, then we can calculate its length:

2a = P – 2b;

a = (P – 2b): 2.

Then the length of the given rectangle will be equal to:

a = (42 – 2 * 6): 2;

a = (42 – 12): 2;

a = 30: 2;

a = 15 (cm).

Answer: The length of the rectangle is 15 cm.