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Intermediate

The colour of spring

A square with a diagonal and a right angle. Two areas are given. How large is the pink area?

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Solution

The area is 2.

First draw horizontal and vertical line segments through the intersection point as shown. From the 1 : 2 proportion of the given areas we infer the the lengths on the right.

Now from rotational symmetry we can find two similar triangles as shown and because their middle sides both equal 2a they are also congruent. The areas can now be filled in and because 3A=6 we find A=2.

Poem

The colour of Spring
The air is warming
The birds are singing
Spring is coming
It’s winter sleep is ending
The tulips are growing
And we are planting
The air is changing
Pink, green, blue and yellow painting
The tulip is wondering
Why is the rose smelling ?

Bella

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