Question

A square piece of paper is folded in half. The folded paper is then cut in half by a straight cut parallel to the fold. This forms three rectangles: one large rectangle and two small ones. What is the ratio of the perimeter of one of the small rectangles to the perimeter of the large rectangle?

$\dfrac{1}{2}$

$\dfrac{2}{3}$

$\dfrac{3}{4}$

$\dfrac{4}{5}$

$\dfrac{5}{6}$

Answer: E

Concepts:paper folding perimeter

Difficulty rating: 950

Solution:

Let the square have side $4.$ Folding in half makes a $2 \times 4$ stack of two layers. Cutting parallel to the fold splits it into a strip containing the fold and a strip that does not.

The strip with the fold unfolds into the large rectangle, $2 \times 4,$ with perimeter $2(2 + 4) = 12.$ The other strip is two separate small rectangles, each $1 \times 4,$ with perimeter $2(1 + 4) = 10.$ The ratio is $\frac{10}{12} = \frac{5}{6}.$

Thus, the correct answer is E .

1989 AMC 8 Problem 24

Answer: E

Solution:

Problem 24 in Other Years