Write and simplify an expression for the perimeter of a rectangle if the length is 6 cm longer than three times the width.

Let width be w; and length be l.

By given information, l = 6 + 3*w

Hence, perimeter of rectangle = 2 * (l+w) = 2 * (6 + 3w + w) = 2 * (6 + 4w) = 12 + 8w

P = 8w+12. Perimeter of a rectangle is equal to twice the length plus twice the width, or P = 2l + 2w. If the length is 3 times the width plus 6, the length can be written as 3w+6. P=2l + 2w so plug in 3w+6 for the length to get P=2 (3w+6) + 2w. Simplify and P = 8w+12.