Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

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

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

etc

Answer 4

Oh, did no. notice the "in half"