1986 AMC 12 Problem 6

Question

Using a table of a certain height, two identical blocks of wood are placed as shown in Figure

1.

Length

r

is found to be

32

inches. After rearranging the blocks as in Figure

2,

length

s

is found to be

28

inches. How high is the table?

28

inches

29

inches

30

inches

31

inches

32

inches

Let

h

be the table height and let the block dimensions be

\ell

and

w

Write one vertical-distance equation for each figure and add them

Let

h

be the table height and let

\ell,w

be the long and short block dimensions. Figure

1

gives

h+\ell-w=32,

while Figure

2

gives

h+w-\ell=28.

Adding cancels the block dimensions:

2h=60,

so

h=30

inches.

Thus the correct answer is C.

Problem 6 in other years