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?

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 
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 
Damon
a(a+b) = 100
but
b = 2a/(1+sqrt5)
a [ a + 2a/(1+sqrt5) ]=100
a^2 [ 1 +2/(1+sqrt5) ] = 100
etc 
Damon
Oh, did no. notice the "in half"
Respond to this Question
Similar Questions

Math
If you fold a normal piece of paper in half and then fold that in half and then fold that in half etc and repeat the folding 50 times, How thick is your final result? 
English expression
I will distribute a piece of paper to each of you. Hand down the pieces of paper (In a line composed of two people in each row.). Pass them to the students back. Do you have a piece of paper? 
Math
Sophie measured a piece of paper to be 21.7 cm by 28.5 cm. The piece of paper is actually 21.6 cm by 28.4 cm. Determine the amount of square centimeters in the area of the piece of paper using Sophie's measurements.(I got 618.45 sq … 
8th grade math
Jessica is creating a heartshaped card to give to her valentine. She has folded a square piece of paper in half and traced the pattern onto one half of the folded paper. The pattern consists of a right triangle with hypotenuse of … 
math
When a square piece of paper is folded in half vertically, the resulting rectangle has a perimeter of 39cm. In square centimeters, find the area of the original square piece of paper. 
Math
A piece of paper is cut into 25 equal parts that are similar in shape to the original. what is the perimeter of one of the small pieces divided by the perimeter of the original piece of paper? 
Maths
a rectangular piece of paper has length=14cm and breadth=12cm. A square piece of paper of perimeter 24 cm is cut off from it. what is the area of the piece of paper left 
Math
A square piece of paper is folded in half to make a rectangle. The perimeter of the rectangle is 24.9 cm. What is the side length of the square piece of paper? 
math help
A piece of rectangular paper measures 8x by 12x. If a circle with a radius of 3x is cut out of the middle of the paper, what will be the area of the remaining piece of paper in terms of π? 
math
an artist buys a rectangular piece of paper for his artwork. he cuts the piece of paper into 8 equal strips. he uses 6 strips of paper and keeps the rest. what fraction of the rectangular piece of paper did he use?