# maths

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We can cut a square diagonally in half to get two triangles. Suppose the
perimeter of the square is 3cm longer than the perimeter of a resulting triangle.
What is the perimeter of the square?

• maths -

Let a-the side of the square, then
sqrt(a^2+a^2)=a*sqrt(2)-diagonal.
On the condition of the problem
4a=2a+a*sqrt(2)+3
a(2-sqrt(2))=3
a=3/(2-sqrt(2))=3(2+sqrt(2))/2
The perimeter of the square=4a=6(2+sqrt(2))=20.49cm

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