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

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## Solution

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

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

## 2 replies on “Emerging from water”

Solution

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