¶ 2020 AMC8 Problem 25
Problem:
Rectangles and , and squares , , and , shown below, combine to form a rectangle that is units wide and units high. What is the side length of in units?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and represent the side lengths of squares and , respectively. Then the width of the large rectangle equals
and the height of the large rectangle equals
Subtracting the two equations yields , so The side length of is therefore units.
: Although the size of square is fixed, the sizes of and can vary as long as the sum of their side lengths is .
Problems and Solutions contributed by Hannah Alpert, Bela Bajnok, Helen Beylkin, Silva Chang, Barbara Currier, Dotty Dady, Tivadar Diveki, Steven Dunbar, Marta Eso, Chris Jeuell, Steven Klee, Rich Morrow, Bryan Nevarez, Daheng Shen, Jeganathan Sriskandarajah, Zsuzsanna Szaniszlo, David Wells, Carl Yerger, and Jesse Zhang.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions