Maths Olympiad Prep

Track / Stage 4 / 334 of 340 #594 of 1964

Problem 594

AMC 12 late, AIME early
Geometry Difficulty 5.0 Find the answer

## Task 1 - 300521

a) The figure shows a decomposition of a square by straight cuts into four sub-figures.

Indicate how these sub-figures can be combined to form two equal-sized squares! A drawing of the two newly assembled squares is sufficient as a solution.

!

b) Determine whether a square can be decomposed by straight cuts into six sub-figures such that they can be combined to form two equal-sized squares!

If such a decomposition is possible, a drawing of such a decomposition and the two newly assembled squares is sufficient as a solution.

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

Official solution

The illustrations a, b each show drawings of the required type. There are several other possibilities.
!

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.