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

Scroll down for a solution to this problem.

## Solution

The proportion green : blue is 5 : 16.

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