MathDB

F 1

Source:

May 25, 2007

geometryrectangleinductionrational numbers

Problem Statement

Suppose that a rectangle with sides

a

and

b

is arbitrarily cut into

n

squares with sides

x_{1},\ldots,x_{n}

. Show that

\frac{x_{i}}{a}\in\mathbb{Q}

and

\frac{x_{i}}{b}\in\mathbb{Q}

for all

i\in\{1,\cdots, n\}

.

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