Question

A rectangular picture with perimeter 27 cm is glued in the center of a rectangular piece of cardboard. There is a 1 cm margin ( of empty cardboard) all around the picture. What is the perimeter of the piece of cardboard.

Answer 1

35 cm

Explanation:

Each dimension of the picture is increased by twice the width of the margin. If the original picture has dimensions L×W, then the cardboard has dimensions (L+2)×(W+2).

The perimeter formula tells you the perimeter is ...

P = 2(L +W)

__

The cardboard perimeter will be ...

P' = 2((L +2) +(W +2)) = 2(L +W +4)

P' = 2(L +W) +8

P' = P +8

If the original perimeter is 27 cm, the cardboard perimeter is ...

P' = 27 +8 = 35 . . . . cm

The perimeter of the cardboard is 35 cm.