# Maths: Surds

posted by Ripley

A rectangular piece of paper has an area of 100 rt2 cm^2. The piece of paper is such that, when it is folded in half along the dashed line, the new rectangle is similar (of the same shape) to the original rectangle. What are the dimensions of the piece of paper?

1. Damon

I do not see your picture but suspect you are talking about what is often called the "golden ratio".
http://en.wikipedia.org/wiki/Golden_ratio

2. Steve

if the length is x and the height is y, we need

y/x = (x/2)/y
x^2 = 2y^2
x = √2 y

since xy = 100√2
y=10
x=10√2

3. Damon

a(a+b) = 100
but
b = 2a/(1+sqrt5)

a [ a + 2a/(1+sqrt5) ]=100

a^2 [ 1 +2/(1+sqrt5) ] = 100

etc

4. Damon

Oh, did no. notice the "in half"

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