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Intermediate

Emerging from water

Two squares and an extended side. What’s red : green : pink?

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Solution

Red : green : pink is 4 : 5 : 3.

Solution by Ferdi Yılmaztürk.

This solution uses the result from The baby block.

Poem

Emerging from water
A block of ice
A bluish iceberg .
Like any submerged body
Takes a push of Archimede .
An object can float
It’s just known as a
Principle of physics
And buoyancy
Archimedes got his spiral
Who lives in the circle
Eureka !
Archimedes found
An idea has emerged

Bella

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2 replies on “Emerging from water”

Let ABCD clockwise with A at top left corner be the big square and PQRS clockwise be the small square with P as midpoint of BC. Let the big and small square sides be 2 and x respectively.

Clearly all five small triangles are similar right angled triangles.
PC=1, DC=2 gives DP=√5
RQ=x, DQ=x/2 gives DR=(√5/2)*x
Also DQ+QP=x/2 + x = (3/2)*x =√5.
Hence x=(2/3)*√5 and DR=5/3
Hence AR=1/3 and AM=2/3
As BP=1, NB=1/2
Finally MN=2-(2/3)-(1/2)=5/6
The ratio = AM:MN:NB
= 2/3 : 5/6 : 1/2
= 4:5:3

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