Geometry & Figures

Problem

Ribbon length matches parallel box edges

A rectangular box that is 12 cm wide, 8 cm deep, and 15 cm tall is wrapped with ribbon. The ribbon makes one full loop around the box in each of two perpendicular directions, passing over the top and bottom and down the sides, and a bow at the top uses 30 cm. We want the total length of ribbon used.
12 cm 8 cm 15 cm
GeometryMeasurement & data
Your answer
How to solve
Strategy Draw a Diagram — Sketching the box and tracing where the ribbon lies shows that every straight stretch of ribbon runs parallel to a box edge, so its length is just that edge length. Breaking the wrapping into the two loops (and grouping the pieces by direction) turns a 3-D puzzle into simple addition of edge lengths, then we add the 30 cm bow at the end.
1STEP 1

See that ribbon pieces match box edges

Each straight run of ribbon lies flat along a box edge, so it is exactly that edge's length.

2STEP 2

Length of the first loop

The first loop goes right around one face, covering two widths and two heights: 54 cm.

2 × 12 + 2 × 15 = 24 + 30 = 54
3STEP 3

Length of the second loop

The second loop wraps the other face, covering two depths and two heights: 46 cm.

2 × 8 + 2 × 15 = 16 + 30 = 46
4STEP 4

Add the two loops

Add the ribbon used by the two loops to get the length that actually goes around the box.

54 + 46 = 100
5STEP 5

Add the bow

Finally, add the 30 cm used for the bow (knot) on the top.

100 + 30 = 130
Answer
130 cm
The answer is a length in cm, which fits. Each loop is a little more than 4 sides, and 54 + 46 = 100 cm of wrapping plus a 30 cm bow gives 130 cm — a sensible amount of ribbon for a box this size.
Takeaway

Ribbon pressed flat along a box is as long as the edge it follows, so just add up the edges it covers — then add the bow.

  • See that ribbon pieces match box edges
  • Length of the first loop
  • Length of the second loop
  • Add the two loops
  • Add the bow
Where next?
Another one like thissuggested

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