2014 UNCO Math Contest II Problems/Problem 5

Problem

(a) The White Rabbit has a square garden with sides of length one meter. He builds a square cucumber frame in the center by connecting each corner of the garden to the midpoint of a far side of the garden, going clockwise, as shown in the diagram. What is the area of the region that is enclosed in the inner square frame?

(b) Suppose that the White Rabbit builds his square cucumber frame by connecting each corner of the garden to a point a distance $x$ from the next corner, going clockwise, as shown in the diagram. Now what is the area of the region that is enclosed in the inner square frame?

Solution

(a) $\frac{1}{5}$ (b) $\frac{(1-x)^2}{1+x^2}$

2014 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10
All UNCO Math Contest Problems and Solutions

Page

Toolbox

Search

2014 UNCO Math Contest II Problems/Problem 5

Problem

Solution

See also