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4 equal rectangles

Ariel Marcy

13 September, 2023

Difficulty: Fun

The big rectangle below is made from 4 small rectangles. All the small rectangles are equal, meaning that they have the same size and shape.

If the small rectangle’s short side is 8 centimetres, what is the length (long side) of the bigger rectangle?

Rectangle with H shaped lines inside creating four new rectangles.

Scroll down or click for a hint, or the answer!

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Brainteaser hint

Remember that all the small rectangles have the same dimensions.
Where else can you label “8 cm” on the diagram?

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Brainteaser answer

The length (long side) of the bigger rectangle is 32 centimetres.

The key to solving this geometry problem lies in the title: 4 equal rectangles. We know from the problem that the short side of all the small rectangles is 8 centimetres. This includes the middle rectangles lying in the centre, if we label their short sides as 8 centimetres we get:

Rectangle broken into four smaller rectangles with dimensions 8 x 16 cm

Now we know the long side of the small rectangles is 8 + 8 = 16 centimetres. Since the small rectangles are all equal, this dimension must be true for all of them.

The next step is to add up all the lengths along the long side of the bigger rectangle:

Bigger rectangle width = short side of small rectangle + long side of small rectangle + short side of small rectangle

= 8 + 16 + 8

= 32 centimetres.

Rectangle broken into four smaller rectangles with dimensions marked.

Categories:

Brainteaser, Maths

Tags:

mathematical sciences, number, problem solving

6 responses

Mark

15 September, 2023

The length of the rectangle is 32 cms, and the width is 16 cms.

Reply
Norman

15 September, 2023

I agree with Mark, width is usually the shorter of the two distances, whether the shape is displayed in portrait or landscape.

Reply
Peter

17 September, 2023

Since height or length are not specified, then width is open to interpretation. You could see it as a window, so horizontal width, or as a tennis court, so narrow width. Good observation for Mark and Norman.

Reply
Ariel Marcy

18 September, 2023

Thanks for the keen edits! We’ve updated the problem to use length and long side so there’s no confusion.

Reply
Mark

18 September, 2023

Thank you for making the correction. However, you have not changed the original question on the opening page. You still ask, ‘ . . . what is the width (of) the big rectangle?’
It should be ‘. . . what is the length of the bigger rectangle.’ Or, if you prefer, ‘. . . what is the length (long side) of the bigger rectangle?’

Reply
1. David Shaw
  
  22 September, 2023
  
  updated!
  
  Reply