Problem
This loop covers two 30 cm edges and two 40 cm heights, for 140 cm.
Wrapping once around traces a rectangle with the 30 cm edge on top and bottom and the 40 cm height on each side; since opposite sides match, adding each length twice gives the whole loop.
Draw A Diagram3.MD.D.8Measuring LengthThe ribbon loop that wraps the box in the 30 cm direction measures 140 cm, because it covers the 30 cm edge twice and the 40 cm height twice (30 + 40 + 30 + 40).
Wrapped once around, the ribbon traces an upright rectangle whose top and bottom are the 30 cm edge and whose two sides are the 40 cm height.
A rectangle's opposite sides are always the same length, so the loop has two 30 cm sides and two 40 cm sides.
The whole loop's length is just its four straight pieces added together.
The four pieces meet end to end with no gaps or overlaps, so their lengths add back to make the whole loop.
This loop covers two 35 cm edges and two 40 cm heights, for 150 cm.
The same loop idea now applies to the 35 cm edge: two 35 cm edges plus two 40 cm heights give that direction's loop length.
Draw A Diagram3.MD.D.8Measuring Length140+150+45=335 cm, and 100 cm make 1 m, so the total is 3 m 35 cm.
The total ribbon is both loops plus the bow. Grouping 335 cm into hundreds gives three 1 m bundles with 35 cm left over — 3 m 35 cm.
Identify Subproblems2.MD.B.5Measuring LengthEach wrap of ribbon is just the perimeter of a rectangle around the box. Add both loops and the bow to get the total ribbon length.