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Intermediate

The holiday home

An isosceles triangle, a rectangle and two diagonals. What is the proportion green : blue?

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Solution

The proportion green : blue is 5 : 16.

Solution by øw415.

The fastest solution uses the fact that the five vertices lie on a circle of radius 5 as shown above. Using the fact that equal chords have equal angles it is evident that both triangles are similar. Their areas therefore are proportioned as the square of corresponding sides. In this case 20/64.

Poem

It can be a shelter
Where you can go or enter
It can be the house for holidays time
With flowers, water, sand and doorbell chime
It’s not a haunt but surely a home
Open for all the guests who want to come
A house with comfort everyday
With nice greetings when you’ve been away

Bella

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