1988 AHSME Problems/Problem 9
Problem
An table sits in the corner of a square room, as in Figure below. The owners desire to move the table to the position shown in Figure . The side of the room is feet. What is the smallest integer value of for which the table can be moved as desired without tilting it or taking it apart?
Solution
Small correction: The writer below has maximized the area of the rectangle (with sides parallel to the walls) that fits around the table, but there is a larger single dimension we can find in the table. The height or width is maximized when the diagonal of the table is horizontal or vertical. By the Pythagorean Theorem, this diagonal is which is between and so the answer is still -hailstone
We begin by thinking about the motion of the table. As it moves, the table will have it's maximum height and width when the rectangle's sides form degree angles relative to the sides of the square. Therefore, by the Pythagorean Theorem, we have that , with being the length of the leg formed by the side of the square with length and being the length of the leg formed by the side of the square with length . Adding these up yields .
We have that . That means that , which rounds up to .
See also
1988 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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